Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,3,Mod(31,60)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(60, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("60.31");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.63488158616\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.85100625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 2x^{6} + x^{5} + 3x^{4} + 2x^{3} - 8x^{2} - 8x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 31.5 | ||
Root | \(-0.600040 - 1.28061i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 60.31 |
Dual form | 60.3.c.a.31.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(37\) | \(41\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.67986 | − | 1.08539i | 0.839931 | − | 0.542693i | ||||
\(3\) | 1.73205i | 0.577350i | ||||||||
\(4\) | 1.64388 | − | 3.64660i | 0.410969 | − | 0.911649i | ||||
\(5\) | 2.23607 | 0.447214 | ||||||||
\(6\) | 1.87994 | + | 2.90961i | 0.313324 | + | 0.484935i | ||||
\(7\) | 0.596540i | 0.0852199i | 0.999092 | + | 0.0426100i | \(0.0135673\pi\) | ||||
−0.999092 | + | 0.0426100i | \(0.986433\pi\) | |||||||
\(8\) | −1.19648 | − | 7.91002i | −0.149560 | − | 0.988753i | ||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 3.75629 | − | 2.42700i | 0.375629 | − | 0.242700i | ||||
\(11\) | 9.27963i | 0.843602i | 0.906688 | + | 0.421801i | \(0.138602\pi\) | ||||
−0.906688 | + | 0.421801i | \(0.861398\pi\) | |||||||
\(12\) | 6.31609 | + | 2.84728i | 0.526341 | + | 0.237273i | ||||
\(13\) | −23.5117 | −1.80859 | −0.904295 | − | 0.426907i | \(-0.859603\pi\) | ||||
−0.904295 | + | 0.426907i | \(0.859603\pi\) | |||||||
\(14\) | 0.647476 | + | 1.00210i | 0.0462483 | + | 0.0715789i | ||||
\(15\) | 3.87298i | 0.258199i | ||||||||
\(16\) | −10.5953 | − | 11.9891i | −0.662209 | − | 0.749319i | ||||
\(17\) | 3.97751 | 0.233971 | 0.116986 | − | 0.993134i | \(-0.462677\pi\) | ||||
0.116986 | + | 0.993134i | \(0.462677\pi\) | |||||||
\(18\) | −5.03959 | + | 3.25616i | −0.279977 | + | 0.180898i | ||||
\(19\) | − | 7.04756i | − | 0.370924i | −0.982651 | − | 0.185462i | \(-0.940622\pi\) | ||
0.982651 | − | 0.185462i | \(-0.0593782\pi\) | |||||||
\(20\) | 3.67582 | − | 8.15404i | 0.183791 | − | 0.407702i | ||||
\(21\) | −1.03324 | −0.0492018 | ||||||||
\(22\) | 10.0720 | + | 15.5885i | 0.457817 | + | 0.708568i | ||||
\(23\) | 32.0793i | 1.39475i | 0.716705 | + | 0.697376i | \(0.245649\pi\) | ||||
−0.716705 | + | 0.697376i | \(0.754351\pi\) | |||||||
\(24\) | 13.7006 | − | 2.07237i | 0.570857 | − | 0.0863486i | ||||
\(25\) | 5.00000 | 0.200000 | ||||||||
\(26\) | −39.4964 | + | 25.5192i | −1.51909 | + | 0.981509i | ||||
\(27\) | − | 5.19615i | − | 0.192450i | ||||||
\(28\) | 2.17534 | + | 0.980637i | 0.0776907 | + | 0.0350227i | ||||
\(29\) | 35.6734 | 1.23012 | 0.615059 | − | 0.788481i | \(-0.289132\pi\) | ||||
0.615059 | + | 0.788481i | \(0.289132\pi\) | |||||||
\(30\) | 4.20368 | + | 6.50608i | 0.140123 | + | 0.216869i | ||||
\(31\) | − | 59.2585i | − | 1.91156i | −0.294076 | − | 0.955782i | \(-0.595012\pi\) | ||
0.294076 | − | 0.955782i | \(-0.404988\pi\) | |||||||
\(32\) | −30.8115 | − | 8.64000i | −0.962860 | − | 0.270000i | ||||
\(33\) | −16.0728 | −0.487054 | ||||||||
\(34\) | 6.68167 | − | 4.31713i | 0.196520 | − | 0.126974i | ||||
\(35\) | 1.33390i | 0.0381115i | ||||||||
\(36\) | −4.93163 | + | 10.9398i | −0.136990 | + | 0.303883i | ||||
\(37\) | −5.38761 | −0.145611 | −0.0728055 | − | 0.997346i | \(-0.523195\pi\) | ||||
−0.0728055 | + | 0.997346i | \(0.523195\pi\) | |||||||
\(38\) | −7.64932 | − | 11.8389i | −0.201298 | − | 0.311551i | ||||
\(39\) | − | 40.7234i | − | 1.04419i | ||||||
\(40\) | −2.67541 | − | 17.6873i | −0.0668853 | − | 0.442184i | ||||
\(41\) | 40.0791 | 0.977539 | 0.488769 | − | 0.872413i | \(-0.337446\pi\) | ||||
0.488769 | + | 0.872413i | \(0.337446\pi\) | |||||||
\(42\) | −1.73570 | + | 1.12146i | −0.0413261 | + | 0.0267014i | ||||
\(43\) | 36.1157i | 0.839901i | 0.907547 | + | 0.419950i | \(0.137953\pi\) | ||||
−0.907547 | + | 0.419950i | \(0.862047\pi\) | |||||||
\(44\) | 33.8391 | + | 15.2545i | 0.769070 | + | 0.346694i | ||||
\(45\) | −6.70820 | −0.149071 | ||||||||
\(46\) | 34.8184 | + | 53.8888i | 0.756922 | + | 1.17150i | ||||
\(47\) | − | 74.0131i | − | 1.57475i | −0.616477 | − | 0.787373i | \(-0.711441\pi\) | ||
0.616477 | − | 0.787373i | \(-0.288559\pi\) | |||||||
\(48\) | 20.7657 | − | 18.3517i | 0.432620 | − | 0.382327i | ||||
\(49\) | 48.6441 | 0.992738 | ||||||||
\(50\) | 8.39931 | − | 5.42693i | 0.167986 | − | 0.108539i | ||||
\(51\) | 6.88925i | 0.135083i | ||||||||
\(52\) | −38.6503 | + | 85.7376i | −0.743275 | + | 1.64880i | ||||
\(53\) | −2.55123 | −0.0481364 | −0.0240682 | − | 0.999710i | \(-0.507662\pi\) | ||||
−0.0240682 | + | 0.999710i | \(0.507662\pi\) | |||||||
\(54\) | −5.63983 | − | 8.72882i | −0.104441 | − | 0.161645i | ||||
\(55\) | 20.7499i | 0.377270i | ||||||||
\(56\) | 4.71864 | − | 0.713748i | 0.0842614 | − | 0.0127455i | ||||
\(57\) | 12.2067 | 0.214153 | ||||||||
\(58\) | 59.9265 | − | 38.7194i | 1.03321 | − | 0.667576i | ||||
\(59\) | 36.4026i | 0.616993i | 0.951225 | + | 0.308497i | \(0.0998259\pi\) | ||||
−0.951225 | + | 0.308497i | \(0.900174\pi\) | |||||||
\(60\) | 14.1232 | + | 6.36670i | 0.235387 | + | 0.106112i | ||||
\(61\) | −8.73223 | −0.143151 | −0.0715757 | − | 0.997435i | \(-0.522803\pi\) | ||||
−0.0715757 | + | 0.997435i | \(0.522803\pi\) | |||||||
\(62\) | −64.3183 | − | 99.5461i | −1.03739 | − | 1.60558i | ||||
\(63\) | − | 1.78962i | − | 0.0284066i | ||||||
\(64\) | −61.1369 | + | 18.9284i | −0.955264 | + | 0.295756i | ||||
\(65\) | −52.5737 | −0.808826 | ||||||||
\(66\) | −27.0001 | + | 17.4452i | −0.409092 | + | 0.264321i | ||||
\(67\) | 69.7379i | 1.04086i | 0.853903 | + | 0.520432i | \(0.174229\pi\) | ||||
−0.853903 | + | 0.520432i | \(0.825771\pi\) | |||||||
\(68\) | 6.53853 | − | 14.5044i | 0.0961548 | − | 0.213300i | ||||
\(69\) | −55.5630 | −0.805261 | ||||||||
\(70\) | 1.44780 | + | 2.24077i | 0.0206828 | + | 0.0320110i | ||||
\(71\) | − | 59.2170i | − | 0.834043i | −0.908897 | − | 0.417021i | \(-0.863074\pi\) | ||
0.908897 | − | 0.417021i | \(-0.136926\pi\) | |||||||
\(72\) | 3.58944 | + | 23.7301i | 0.0498534 | + | 0.329584i | ||||
\(73\) | −83.0019 | −1.13701 | −0.568506 | − | 0.822679i | \(-0.692478\pi\) | ||||
−0.568506 | + | 0.822679i | \(0.692478\pi\) | |||||||
\(74\) | −9.05044 | + | 5.84763i | −0.122303 | + | 0.0790220i | ||||
\(75\) | 8.66025i | 0.115470i | ||||||||
\(76\) | −25.6996 | − | 11.5853i | −0.338153 | − | 0.152438i | ||||
\(77\) | −5.53566 | −0.0718917 | ||||||||
\(78\) | −44.2006 | − | 68.4098i | −0.566675 | − | 0.877048i | ||||
\(79\) | 65.8705i | 0.833804i | 0.908951 | + | 0.416902i | \(0.136884\pi\) | ||||
−0.908951 | + | 0.416902i | \(0.863116\pi\) | |||||||
\(80\) | −23.6919 | − | 26.8085i | −0.296149 | − | 0.335106i | ||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 67.3274 | − | 43.5013i | 0.821065 | − | 0.530503i | ||||
\(83\) | 129.909i | 1.56517i | 0.622542 | + | 0.782586i | \(0.286100\pi\) | ||||
−0.622542 | + | 0.782586i | \(0.713900\pi\) | |||||||
\(84\) | −1.69851 | + | 3.76780i | −0.0202204 | + | 0.0448547i | ||||
\(85\) | 8.89398 | 0.104635 | ||||||||
\(86\) | 39.1995 | + | 60.6695i | 0.455808 | + | 0.705459i | ||||
\(87\) | 61.7882i | 0.710209i | ||||||||
\(88\) | 73.4020 | − | 11.1029i | 0.834114 | − | 0.126169i | ||||
\(89\) | −130.466 | −1.46591 | −0.732956 | − | 0.680277i | \(-0.761860\pi\) | ||||
−0.732956 | + | 0.680277i | \(0.761860\pi\) | |||||||
\(90\) | −11.2689 | + | 7.28099i | −0.125210 | + | 0.0808999i | ||||
\(91\) | − | 14.0256i | − | 0.154128i | ||||||
\(92\) | 116.980 | + | 52.7344i | 1.27152 | + | 0.573200i | ||||
\(93\) | 102.639 | 1.10364 | ||||||||
\(94\) | −80.3327 | − | 124.332i | −0.854603 | − | 1.32268i | ||||
\(95\) | − | 15.7588i | − | 0.165882i | ||||||
\(96\) | 14.9649 | − | 53.3671i | 0.155885 | − | 0.555908i | ||||
\(97\) | 93.1113 | 0.959911 | 0.479955 | − | 0.877293i | \(-0.340653\pi\) | ||||
0.479955 | + | 0.877293i | \(0.340653\pi\) | |||||||
\(98\) | 81.7155 | − | 52.7977i | 0.833831 | − | 0.538752i | ||||
\(99\) | − | 27.8389i | − | 0.281201i | ||||||
\(100\) | 8.21938 | − | 18.2330i | 0.0821938 | − | 0.182330i | ||||
\(101\) | −3.66081 | −0.0362457 | −0.0181228 | − | 0.999836i | \(-0.505769\pi\) | ||||
−0.0181228 | + | 0.999836i | \(0.505769\pi\) | |||||||
\(102\) | 7.47749 | + | 11.5730i | 0.0733087 | + | 0.113461i | ||||
\(103\) | − | 151.417i | − | 1.47007i | −0.678032 | − | 0.735033i | \(-0.737167\pi\) | ||
0.678032 | − | 0.735033i | \(-0.262833\pi\) | |||||||
\(104\) | 28.1313 | + | 185.978i | 0.270493 | + | 1.78825i | ||||
\(105\) | −2.31039 | −0.0220037 | ||||||||
\(106\) | −4.28571 | + | 2.76907i | −0.0404313 | + | 0.0261233i | ||||
\(107\) | − | 82.8092i | − | 0.773918i | −0.922097 | − | 0.386959i | \(-0.873526\pi\) | ||
0.922097 | − | 0.386959i | \(-0.126474\pi\) | |||||||
\(108\) | −18.9483 | − | 8.54183i | −0.175447 | − | 0.0790910i | ||||
\(109\) | −7.36835 | −0.0675996 | −0.0337998 | − | 0.999429i | \(-0.510761\pi\) | ||||
−0.0337998 | + | 0.999429i | \(0.510761\pi\) | |||||||
\(110\) | 22.5216 | + | 34.8569i | 0.204742 | + | 0.316881i | ||||
\(111\) | − | 9.33161i | − | 0.0840685i | ||||||
\(112\) | 7.15197 | − | 6.32054i | 0.0638569 | − | 0.0564334i | ||||
\(113\) | 65.0370 | 0.575549 | 0.287774 | − | 0.957698i | \(-0.407085\pi\) | ||||
0.287774 | + | 0.957698i | \(0.407085\pi\) | |||||||
\(114\) | 20.5056 | − | 13.2490i | 0.179874 | − | 0.116219i | ||||
\(115\) | 71.7315i | 0.623752i | ||||||||
\(116\) | 58.6427 | − | 130.087i | 0.505540 | − | 1.12144i | ||||
\(117\) | 70.5350 | 0.602864 | ||||||||
\(118\) | 39.5109 | + | 61.1514i | 0.334838 | + | 0.518232i | ||||
\(119\) | 2.37274i | 0.0199390i | ||||||||
\(120\) | 30.6354 | − | 4.63395i | 0.255295 | − | 0.0386163i | ||||
\(121\) | 34.8885 | 0.288335 | ||||||||
\(122\) | −14.6689 | + | 9.47784i | −0.120237 | + | 0.0776872i | ||||
\(123\) | 69.4190i | 0.564382i | ||||||||
\(124\) | −216.092 | − | 97.4136i | −1.74268 | − | 0.785593i | ||||
\(125\) | 11.1803 | 0.0894427 | ||||||||
\(126\) | −1.94243 | − | 3.00631i | −0.0154161 | − | 0.0238596i | ||||
\(127\) | − | 139.469i | − | 1.09818i | −0.835763 | − | 0.549091i | \(-0.814974\pi\) | ||
0.835763 | − | 0.549091i | \(-0.185026\pi\) | |||||||
\(128\) | −82.1569 | + | 98.1542i | −0.641851 | + | 0.766829i | ||||
\(129\) | −62.5543 | −0.484917 | ||||||||
\(130\) | −88.3166 | + | 57.0628i | −0.679359 | + | 0.438944i | ||||
\(131\) | 63.4856i | 0.484623i | 0.970198 | + | 0.242312i | \(0.0779056\pi\) | ||||
−0.970198 | + | 0.242312i | \(0.922094\pi\) | |||||||
\(132\) | −26.4217 | + | 58.6110i | −0.200164 | + | 0.444023i | ||||
\(133\) | 4.20415 | 0.0316101 | ||||||||
\(134\) | 75.6925 | + | 117.150i | 0.564870 | + | 0.874254i | ||||
\(135\) | − | 11.6190i | − | 0.0860663i | ||||||
\(136\) | −4.75901 | − | 31.4622i | −0.0349927 | − | 0.231340i | ||||
\(137\) | −138.157 | −1.00845 | −0.504223 | − | 0.863573i | \(-0.668221\pi\) | ||||
−0.504223 | + | 0.863573i | \(0.668221\pi\) | |||||||
\(138\) | −93.3382 | + | 60.3073i | −0.676363 | + | 0.437009i | ||||
\(139\) | − | 29.9578i | − | 0.215523i | −0.994177 | − | 0.107762i | \(-0.965632\pi\) | ||
0.994177 | − | 0.107762i | \(-0.0343684\pi\) | |||||||
\(140\) | 4.86421 | + | 2.19277i | 0.0347443 | + | 0.0156626i | ||||
\(141\) | 128.194 | 0.909180 | ||||||||
\(142\) | −64.2733 | − | 99.4765i | −0.452629 | − | 0.700539i | ||||
\(143\) | − | 218.180i | − | 1.52573i | ||||||
\(144\) | 31.7860 | + | 35.9673i | 0.220736 | + | 0.249773i | ||||
\(145\) | 79.7682 | 0.550126 | ||||||||
\(146\) | −139.432 | + | 90.0891i | −0.955012 | + | 0.617048i | ||||
\(147\) | 84.2541i | 0.573157i | ||||||||
\(148\) | −8.85655 | + | 19.6464i | −0.0598416 | + | 0.132746i | ||||
\(149\) | −47.3823 | −0.318002 | −0.159001 | − | 0.987278i | \(-0.550827\pi\) | ||||
−0.159001 | + | 0.987278i | \(0.550827\pi\) | |||||||
\(150\) | 9.39972 | + | 14.5480i | 0.0626648 | + | 0.0969869i | ||||
\(151\) | 109.604i | 0.725852i | 0.931818 | + | 0.362926i | \(0.118222\pi\) | ||||
−0.931818 | + | 0.362926i | \(0.881778\pi\) | |||||||
\(152\) | −55.7463 | + | 8.43227i | −0.366752 | + | 0.0554755i | ||||
\(153\) | −11.9325 | −0.0779904 | ||||||||
\(154\) | −9.29915 | + | 6.00833i | −0.0603841 | + | 0.0390151i | ||||
\(155\) | − | 132.506i | − | 0.854877i | ||||||
\(156\) | −148.502 | − | 66.9442i | −0.951936 | − | 0.429130i | ||||
\(157\) | −177.588 | −1.13113 | −0.565566 | − | 0.824703i | \(-0.691342\pi\) | ||||
−0.565566 | + | 0.824703i | \(0.691342\pi\) | |||||||
\(158\) | 71.4950 | + | 110.653i | 0.452500 | + | 0.700338i | ||||
\(159\) | − | 4.41886i | − | 0.0277916i | ||||||
\(160\) | −68.8967 | − | 19.3196i | −0.430604 | − | 0.120748i | ||||
\(161\) | −19.1366 | −0.118861 | ||||||||
\(162\) | 15.1188 | − | 9.76847i | 0.0933257 | − | 0.0602992i | ||||
\(163\) | − | 96.8778i | − | 0.594342i | −0.954824 | − | 0.297171i | \(-0.903957\pi\) | ||
0.954824 | − | 0.297171i | \(-0.0960432\pi\) | |||||||
\(164\) | 65.8850 | − | 146.152i | 0.401738 | − | 0.891173i | ||||
\(165\) | −35.9398 | −0.217817 | ||||||||
\(166\) | 141.002 | + | 218.230i | 0.849408 | + | 1.31464i | ||||
\(167\) | 152.605i | 0.913801i | 0.889518 | + | 0.456901i | \(0.151040\pi\) | ||||
−0.889518 | + | 0.456901i | \(0.848960\pi\) | |||||||
\(168\) | 1.23625 | + | 8.17292i | 0.00735862 | + | 0.0486484i | ||||
\(169\) | 383.799 | 2.27100 | ||||||||
\(170\) | 14.9407 | − | 9.65340i | 0.0878862 | − | 0.0567847i | ||||
\(171\) | 21.1427i | 0.123641i | ||||||||
\(172\) | 131.700 | + | 59.3698i | 0.765695 | + | 0.345173i | ||||
\(173\) | 155.773 | 0.900422 | 0.450211 | − | 0.892922i | \(-0.351349\pi\) | ||||
0.450211 | + | 0.892922i | \(0.351349\pi\) | |||||||
\(174\) | 67.0640 | + | 103.796i | 0.385425 | + | 0.596527i | ||||
\(175\) | 2.98270i | 0.0170440i | ||||||||
\(176\) | 111.254 | − | 98.3209i | 0.632127 | − | 0.558641i | ||||
\(177\) | −63.0512 | −0.356221 | ||||||||
\(178\) | −219.165 | + | 141.606i | −1.23126 | + | 0.795540i | ||||
\(179\) | − | 126.001i | − | 0.703915i | −0.936016 | − | 0.351957i | \(-0.885516\pi\) | ||
0.936016 | − | 0.351957i | \(-0.114484\pi\) | |||||||
\(180\) | −11.0275 | + | 24.4621i | −0.0612636 | + | 0.135901i | ||||
\(181\) | −346.725 | −1.91561 | −0.957803 | − | 0.287424i | \(-0.907201\pi\) | ||||
−0.957803 | + | 0.287424i | \(0.907201\pi\) | |||||||
\(182\) | −15.2232 | − | 23.5612i | −0.0836442 | − | 0.129457i | ||||
\(183\) | − | 15.1247i | − | 0.0826485i | ||||||
\(184\) | 253.748 | − | 38.3823i | 1.37906 | − | 0.208599i | ||||
\(185\) | −12.0471 | −0.0651192 | ||||||||
\(186\) | 172.419 | − | 111.403i | 0.926983 | − | 0.598939i | ||||
\(187\) | 36.9098i | 0.197379i | ||||||||
\(188\) | −269.896 | − | 121.668i | −1.43562 | − | 0.647171i | ||||
\(189\) | 3.09971 | 0.0164006 | ||||||||
\(190\) | −17.1044 | − | 26.4727i | −0.0900232 | − | 0.139330i | ||||
\(191\) | 133.159i | 0.697167i | 0.937278 | + | 0.348584i | \(0.113337\pi\) | ||||
−0.937278 | + | 0.348584i | \(0.886663\pi\) | |||||||
\(192\) | −32.7849 | − | 105.892i | −0.170755 | − | 0.551522i | ||||
\(193\) | −136.246 | −0.705940 | −0.352970 | − | 0.935635i | \(-0.614828\pi\) | ||||
−0.352970 | + | 0.935635i | \(0.614828\pi\) | |||||||
\(194\) | 156.414 | − | 101.062i | 0.806259 | − | 0.520937i | ||||
\(195\) | − | 91.0604i | − | 0.466976i | ||||||
\(196\) | 79.9649 | − | 177.386i | 0.407984 | − | 0.905029i | ||||
\(197\) | 74.8945 | 0.380175 | 0.190087 | − | 0.981767i | \(-0.439123\pi\) | ||||
0.190087 | + | 0.981767i | \(0.439123\pi\) | |||||||
\(198\) | −30.2159 | − | 46.7655i | −0.152606 | − | 0.236189i | ||||
\(199\) | 251.605i | 1.26434i | 0.774828 | + | 0.632172i | \(0.217836\pi\) | ||||
−0.774828 | + | 0.632172i | \(0.782164\pi\) | |||||||
\(200\) | −5.98240 | − | 39.5501i | −0.0299120 | − | 0.197751i | ||||
\(201\) | −120.790 | −0.600943 | ||||||||
\(202\) | −6.14966 | + | 3.97339i | −0.0304439 | + | 0.0196703i | ||||
\(203\) | 21.2806i | 0.104831i | ||||||||
\(204\) | 25.1223 | + | 11.3251i | 0.123149 | + | 0.0555150i | ||||
\(205\) | 89.6196 | 0.437169 | ||||||||
\(206\) | −164.346 | − | 254.359i | −0.797794 | − | 1.23475i | ||||
\(207\) | − | 96.2379i | − | 0.464917i | ||||||
\(208\) | 249.114 | + | 281.884i | 1.19767 | + | 1.35521i | ||||
\(209\) | 65.3987 | 0.312913 | ||||||||
\(210\) | −3.88113 | + | 2.50766i | −0.0184816 | + | 0.0119412i | ||||
\(211\) | 228.203i | 1.08153i | 0.841173 | + | 0.540766i | \(0.181865\pi\) | ||||
−0.841173 | + | 0.540766i | \(0.818135\pi\) | |||||||
\(212\) | −4.19390 | + | 9.30331i | −0.0197826 | + | 0.0438835i | ||||
\(213\) | 102.567 | 0.481535 | ||||||||
\(214\) | −89.8799 | − | 139.108i | −0.420000 | − | 0.650038i | ||||
\(215\) | 80.7573i | 0.375615i | ||||||||
\(216\) | −41.1017 | + | 6.21710i | −0.190286 | + | 0.0287829i | ||||
\(217\) | 35.3500 | 0.162903 | ||||||||
\(218\) | −12.3778 | + | 7.99751i | −0.0567790 | + | 0.0366858i | ||||
\(219\) | − | 143.763i | − | 0.656454i | ||||||
\(220\) | 75.6664 | + | 34.1102i | 0.343938 | + | 0.155046i | ||||
\(221\) | −93.5179 | −0.423158 | ||||||||
\(222\) | −10.1284 | − | 15.6758i | −0.0456234 | − | 0.0706118i | ||||
\(223\) | − | 85.9549i | − | 0.385448i | −0.981253 | − | 0.192724i | \(-0.938268\pi\) | ||
0.981253 | − | 0.192724i | \(-0.0617322\pi\) | |||||||
\(224\) | 5.15410 | − | 18.3803i | 0.0230094 | − | 0.0820549i | ||||
\(225\) | −15.0000 | −0.0666667 | ||||||||
\(226\) | 109.253 | − | 70.5902i | 0.483421 | − | 0.312346i | ||||
\(227\) | 282.357i | 1.24386i | 0.783071 | + | 0.621932i | \(0.213652\pi\) | ||||
−0.783071 | + | 0.621932i | \(0.786348\pi\) | |||||||
\(228\) | 20.0663 | − | 44.5130i | 0.0880103 | − | 0.195233i | ||||
\(229\) | 138.263 | 0.603768 | 0.301884 | − | 0.953345i | \(-0.402385\pi\) | ||||
0.301884 | + | 0.953345i | \(0.402385\pi\) | |||||||
\(230\) | 77.8563 | + | 120.499i | 0.338506 | + | 0.523909i | ||||
\(231\) | − | 9.58805i | − | 0.0415067i | ||||||
\(232\) | −42.6826 | − | 282.178i | −0.183977 | − | 1.21628i | ||||
\(233\) | −0.522939 | −0.00224438 | −0.00112219 | − | 0.999999i | \(-0.500357\pi\) | ||||
−0.00112219 | + | 0.999999i | \(0.500357\pi\) | |||||||
\(234\) | 118.489 | − | 76.5577i | 0.506364 | − | 0.327170i | ||||
\(235\) | − | 165.498i | − | 0.704248i | ||||||
\(236\) | 132.746 | + | 59.8413i | 0.562482 | + | 0.253565i | ||||
\(237\) | −114.091 | −0.481397 | ||||||||
\(238\) | 2.57534 | + | 3.98588i | 0.0108208 | + | 0.0167474i | ||||
\(239\) | 73.6928i | 0.308338i | 0.988044 | + | 0.154169i | \(0.0492700\pi\) | ||||
−0.988044 | + | 0.154169i | \(0.950730\pi\) | |||||||
\(240\) | 46.4336 | − | 41.0356i | 0.193473 | − | 0.170982i | ||||
\(241\) | 31.3705 | 0.130168 | 0.0650840 | − | 0.997880i | \(-0.479268\pi\) | ||||
0.0650840 | + | 0.997880i | \(0.479268\pi\) | |||||||
\(242\) | 58.6080 | − | 37.8675i | 0.242182 | − | 0.156477i | ||||
\(243\) | 15.5885i | 0.0641500i | ||||||||
\(244\) | −14.3547 | + | 31.8429i | −0.0588307 | + | 0.130504i | ||||
\(245\) | 108.772 | 0.443966 | ||||||||
\(246\) | 75.3464 | + | 116.614i | 0.306286 | + | 0.474042i | ||||
\(247\) | 165.700i | 0.670850i | ||||||||
\(248\) | −468.736 | + | 70.9016i | −1.89006 | + | 0.285894i | ||||
\(249\) | −225.010 | −0.903653 | ||||||||
\(250\) | 18.7814 | − | 12.1350i | 0.0751257 | − | 0.0485399i | ||||
\(251\) | 78.7478i | 0.313736i | 0.987620 | + | 0.156868i | \(0.0501398\pi\) | ||||
−0.987620 | + | 0.156868i | \(0.949860\pi\) | |||||||
\(252\) | −6.52602 | − | 2.94191i | −0.0258969 | − | 0.0116742i | ||||
\(253\) | −297.684 | −1.17662 | ||||||||
\(254\) | −151.378 | − | 234.289i | −0.595975 | − | 0.922397i | ||||
\(255\) | 15.4048i | 0.0604111i | ||||||||
\(256\) | −31.4772 | + | 254.057i | −0.122958 | + | 0.992412i | ||||
\(257\) | 243.954 | 0.949236 | 0.474618 | − | 0.880192i | \(-0.342586\pi\) | ||||
0.474618 | + | 0.880192i | \(0.342586\pi\) | |||||||
\(258\) | −105.083 | + | 67.8956i | −0.407297 | + | 0.263161i | ||||
\(259\) | − | 3.21392i | − | 0.0124090i | ||||||
\(260\) | −86.4246 | + | 191.715i | −0.332402 | + | 0.737366i | ||||
\(261\) | −107.020 | −0.410039 | ||||||||
\(262\) | 68.9064 | + | 106.647i | 0.263002 | + | 0.407050i | ||||
\(263\) | 102.737i | 0.390635i | 0.980740 | + | 0.195317i | \(0.0625737\pi\) | ||||
−0.980740 | + | 0.195317i | \(0.937426\pi\) | |||||||
\(264\) | 19.2308 | + | 127.136i | 0.0728439 | + | 0.481576i | ||||
\(265\) | −5.70472 | −0.0215273 | ||||||||
\(266\) | 7.06239 | − | 4.56312i | 0.0265503 | − | 0.0171546i | ||||
\(267\) | − | 225.974i | − | 0.846344i | ||||||
\(268\) | 254.306 | + | 114.640i | 0.948903 | + | 0.427763i | ||||
\(269\) | −123.646 | −0.459651 | −0.229825 | − | 0.973232i | \(-0.573816\pi\) | ||||
−0.229825 | + | 0.973232i | \(0.573816\pi\) | |||||||
\(270\) | −12.6110 | − | 19.5182i | −0.0467076 | − | 0.0722898i | ||||
\(271\) | − | 332.371i | − | 1.22646i | −0.789904 | − | 0.613230i | \(-0.789870\pi\) | ||
0.789904 | − | 0.613230i | \(-0.210130\pi\) | |||||||
\(272\) | −42.1431 | − | 47.6868i | −0.154938 | − | 0.175319i | ||||
\(273\) | 24.2931 | 0.0889858 | ||||||||
\(274\) | −232.085 | + | 149.954i | −0.847026 | + | 0.547277i | ||||
\(275\) | 46.3981i | 0.168720i | ||||||||
\(276\) | −91.3386 | + | 202.616i | −0.330937 | + | 0.734115i | ||||
\(277\) | −125.916 | −0.454571 | −0.227286 | − | 0.973828i | \(-0.572985\pi\) | ||||
−0.227286 | + | 0.973828i | \(0.572985\pi\) | |||||||
\(278\) | −32.5157 | − | 50.3249i | −0.116963 | − | 0.181025i | ||||
\(279\) | 177.775i | 0.637188i | ||||||||
\(280\) | 10.5512 | − | 1.59599i | 0.0376829 | − | 0.00569996i | ||||
\(281\) | 52.5628 | 0.187056 | 0.0935281 | − | 0.995617i | \(-0.470186\pi\) | ||||
0.0935281 | + | 0.995617i | \(0.470186\pi\) | |||||||
\(282\) | 215.349 | − | 139.140i | 0.763649 | − | 0.493405i | ||||
\(283\) | − | 199.288i | − | 0.704199i | −0.935963 | − | 0.352100i | \(-0.885468\pi\) | ||
0.935963 | − | 0.352100i | \(-0.114532\pi\) | |||||||
\(284\) | −215.941 | − | 97.3454i | −0.760355 | − | 0.342766i | ||||
\(285\) | 27.2951 | 0.0957722 | ||||||||
\(286\) | −236.809 | − | 366.512i | −0.828004 | − | 1.28151i | ||||
\(287\) | 23.9088i | 0.0833058i | ||||||||
\(288\) | 92.4346 | + | 25.9200i | 0.320953 | + | 0.0900001i | ||||
\(289\) | −273.179 | −0.945258 | ||||||||
\(290\) | 134.000 | − | 86.5793i | 0.462068 | − | 0.298549i | ||||
\(291\) | 161.274i | 0.554205i | ||||||||
\(292\) | −136.445 | + | 302.674i | −0.467276 | + | 1.03656i | ||||
\(293\) | 102.161 | 0.348672 | 0.174336 | − | 0.984686i | \(-0.444222\pi\) | ||||
0.174336 | + | 0.984686i | \(0.444222\pi\) | |||||||
\(294\) | 91.4482 | + | 141.535i | 0.311048 | + | 0.481413i | ||||
\(295\) | 81.3987i | 0.275928i | ||||||||
\(296\) | 6.44617 | + | 42.6161i | 0.0217776 | + | 0.143973i | ||||
\(297\) | 48.2184 | 0.162351 | ||||||||
\(298\) | −79.5957 | + | 51.4281i | −0.267100 | + | 0.172577i | ||||
\(299\) | − | 754.238i | − | 2.52254i | ||||||
\(300\) | 31.5805 | + | 14.2364i | 0.105268 | + | 0.0474546i | ||||
\(301\) | −21.5445 | −0.0715763 | ||||||||
\(302\) | 118.962 | + | 184.119i | 0.393915 | + | 0.609666i | ||||
\(303\) | − | 6.34071i | − | 0.0209264i | ||||||
\(304\) | −84.4939 | + | 74.6713i | −0.277941 | + | 0.245629i | ||||
\(305\) | −19.5259 | −0.0640192 | ||||||||
\(306\) | −20.0450 | + | 12.9514i | −0.0655065 | + | 0.0423248i | ||||
\(307\) | − | 328.391i | − | 1.06968i | −0.844954 | − | 0.534839i | \(-0.820372\pi\) | ||
0.844954 | − | 0.534839i | \(-0.179628\pi\) | |||||||
\(308\) | −9.09994 | + | 20.1863i | −0.0295453 | + | 0.0655401i | ||||
\(309\) | 262.262 | 0.848743 | ||||||||
\(310\) | −143.820 | − | 222.592i | −0.463936 | − | 0.718038i | ||||
\(311\) | − | 95.4377i | − | 0.306874i | −0.988158 | − | 0.153437i | \(-0.950966\pi\) | ||
0.988158 | − | 0.153437i | \(-0.0490342\pi\) | |||||||
\(312\) | −322.123 | + | 48.7248i | −1.03245 | + | 0.156169i | ||||
\(313\) | 550.408 | 1.75849 | 0.879246 | − | 0.476368i | \(-0.158047\pi\) | ||||
0.879246 | + | 0.476368i | \(0.158047\pi\) | |||||||
\(314\) | −298.323 | + | 192.751i | −0.950073 | + | 0.613858i | ||||
\(315\) | − | 4.00171i | − | 0.0127038i | ||||||
\(316\) | 240.203 | + | 108.283i | 0.760137 | + | 0.342668i | ||||
\(317\) | 439.394 | 1.38610 | 0.693051 | − | 0.720889i | \(-0.256266\pi\) | ||||
0.693051 | + | 0.720889i | \(0.256266\pi\) | |||||||
\(318\) | −4.79617 | − | 7.42307i | −0.0150823 | − | 0.0233430i | ||||
\(319\) | 331.036i | 1.03773i | ||||||||
\(320\) | −136.706 | + | 42.3251i | −0.427207 | + | 0.132266i | ||||
\(321\) | 143.430 | 0.446822 | ||||||||
\(322\) | −32.1468 | + | 20.7706i | −0.0998348 | + | 0.0645048i | ||||
\(323\) | − | 28.0317i | − | 0.0867855i | ||||||
\(324\) | 14.7949 | − | 32.8194i | 0.0456632 | − | 0.101294i | ||||
\(325\) | −117.558 | −0.361718 | ||||||||
\(326\) | −105.150 | − | 162.741i | −0.322545 | − | 0.499206i | ||||
\(327\) | − | 12.7624i | − | 0.0390286i | ||||||
\(328\) | −47.9539 | − | 317.026i | −0.146201 | − | 0.966544i | ||||
\(329\) | 44.1517 | 0.134200 | ||||||||
\(330\) | −60.3740 | + | 39.0086i | −0.182951 | + | 0.118208i | ||||
\(331\) | − | 479.922i | − | 1.44992i | −0.688794 | − | 0.724958i | \(-0.741859\pi\) | ||
0.688794 | − | 0.724958i | \(-0.258141\pi\) | |||||||
\(332\) | 473.727 | + | 213.555i | 1.42689 | + | 0.643237i | ||||
\(333\) | 16.1628 | 0.0485370 | ||||||||
\(334\) | 165.635 | + | 256.355i | 0.495913 | + | 0.767530i | ||||
\(335\) | 155.939i | 0.465489i | ||||||||
\(336\) | 10.9475 | + | 12.3876i | 0.0325819 | + | 0.0368678i | ||||
\(337\) | 58.8437 | 0.174610 | 0.0873052 | − | 0.996182i | \(-0.472174\pi\) | ||||
0.0873052 | + | 0.996182i | \(0.472174\pi\) | |||||||
\(338\) | 644.730 | − | 416.570i | 1.90748 | − | 1.23246i | ||||
\(339\) | 112.647i | 0.332293i | ||||||||
\(340\) | 14.6206 | − | 32.4328i | 0.0430017 | − | 0.0953905i | ||||
\(341\) | 549.897 | 1.61260 | ||||||||
\(342\) | 22.9480 | + | 35.5168i | 0.0670993 | + | 0.103850i | ||||
\(343\) | 58.2486i | 0.169821i | ||||||||
\(344\) | 285.676 | − | 43.2118i | 0.830454 | − | 0.125616i | ||||
\(345\) | −124.243 | −0.360123 | ||||||||
\(346\) | 261.677 | − | 169.074i | 0.756293 | − | 0.488653i | ||||
\(347\) | 12.1484i | 0.0350099i | 0.999847 | + | 0.0175049i | \(0.00557228\pi\) | ||||
−0.999847 | + | 0.0175049i | \(0.994428\pi\) | |||||||
\(348\) | 225.317 | + | 101.572i | 0.647462 | + | 0.291874i | ||||
\(349\) | −30.9277 | −0.0886180 | −0.0443090 | − | 0.999018i | \(-0.514109\pi\) | ||||
−0.0443090 | + | 0.999018i | \(0.514109\pi\) | |||||||
\(350\) | 3.23738 | + | 5.01052i | 0.00924965 | + | 0.0143158i | ||||
\(351\) | 122.170i | 0.348063i | ||||||||
\(352\) | 80.1760 | − | 285.919i | 0.227773 | − | 0.812271i | ||||
\(353\) | −288.065 | −0.816048 | −0.408024 | − | 0.912971i | \(-0.633782\pi\) | ||||
−0.408024 | + | 0.912971i | \(0.633782\pi\) | |||||||
\(354\) | −105.917 | + | 68.4348i | −0.299201 | + | 0.193319i | ||||
\(355\) | − | 132.413i | − | 0.372995i | ||||||
\(356\) | −214.470 | + | 475.757i | −0.602444 | + | 1.33640i | ||||
\(357\) | −4.10971 | −0.0115118 | ||||||||
\(358\) | −136.759 | − | 211.664i | −0.382010 | − | 0.591240i | ||||
\(359\) | 663.911i | 1.84933i | 0.380776 | + | 0.924667i | \(0.375657\pi\) | ||||
−0.380776 | + | 0.924667i | \(0.624343\pi\) | |||||||
\(360\) | 8.02624 | + | 53.0620i | 0.0222951 | + | 0.147395i | ||||
\(361\) | 311.332 | 0.862415 | ||||||||
\(362\) | −582.450 | + | 376.330i | −1.60898 | + | 1.03959i | ||||
\(363\) | 60.4287i | 0.166470i | ||||||||
\(364\) | −51.1459 | − | 23.0564i | −0.140511 | − | 0.0633418i | ||||
\(365\) | −185.598 | −0.508487 | ||||||||
\(366\) | −16.4161 | − | 25.4074i | −0.0448527 | − | 0.0694190i | ||||
\(367\) | 6.08529i | 0.0165812i | 0.999966 | + | 0.00829059i | \(0.00263901\pi\) | ||||
−0.999966 | + | 0.00829059i | \(0.997361\pi\) | |||||||
\(368\) | 384.602 | − | 339.891i | 1.04511 | − | 0.923618i | ||||
\(369\) | −120.237 | −0.325846 | ||||||||
\(370\) | −20.2374 | + | 13.0757i | −0.0546957 | + | 0.0353397i | ||||
\(371\) | − | 1.52191i | − | 0.00410218i | ||||||
\(372\) | 168.725 | − | 374.282i | 0.453562 | − | 1.00613i | ||||
\(373\) | −204.741 | −0.548903 | −0.274451 | − | 0.961601i | \(-0.588496\pi\) | ||||
−0.274451 | + | 0.961601i | \(0.588496\pi\) | |||||||
\(374\) | 40.0614 | + | 62.0034i | 0.107116 | + | 0.165784i | ||||
\(375\) | 19.3649i | 0.0516398i | ||||||||
\(376\) | −585.445 | + | 88.5552i | −1.55703 | + | 0.235519i | ||||
\(377\) | −838.742 | −2.22478 | ||||||||
\(378\) | 5.20709 | − | 3.36438i | 0.0137754 | − | 0.00890048i | ||||
\(379\) | − | 402.331i | − | 1.06156i | −0.847510 | − | 0.530780i | \(-0.821899\pi\) | ||
0.847510 | − | 0.530780i | \(-0.178101\pi\) | |||||||
\(380\) | −57.4661 | − | 25.9055i | −0.151227 | − | 0.0681725i | ||||
\(381\) | 241.568 | 0.634036 | ||||||||
\(382\) | 144.529 | + | 223.689i | 0.378348 | + | 0.585573i | ||||
\(383\) | − | 331.751i | − | 0.866191i | −0.901348 | − | 0.433096i | \(-0.857421\pi\) | ||
0.901348 | − | 0.433096i | \(-0.142579\pi\) | |||||||
\(384\) | −170.008 | − | 142.300i | −0.442729 | − | 0.370573i | ||||
\(385\) | −12.3781 | −0.0321510 | ||||||||
\(386\) | −228.875 | + | 147.880i | −0.592941 | + | 0.383109i | ||||
\(387\) | − | 108.347i | − | 0.279967i | ||||||
\(388\) | 153.063 | − | 339.540i | 0.394493 | − | 0.875102i | ||||
\(389\) | −623.310 | −1.60234 | −0.801169 | − | 0.598438i | \(-0.795788\pi\) | ||||
−0.801169 | + | 0.598438i | \(0.795788\pi\) | |||||||
\(390\) | −98.8356 | − | 152.969i | −0.253425 | − | 0.392228i | ||||
\(391\) | 127.596i | 0.326332i | ||||||||
\(392\) | −58.2018 | − | 384.776i | −0.148474 | − | 0.981572i | ||||
\(393\) | −109.960 | −0.279797 | ||||||||
\(394\) | 125.812 | − | 81.2894i | 0.319321 | − | 0.206318i | ||||
\(395\) | 147.291i | 0.372889i | ||||||||
\(396\) | −101.517 | − | 45.7636i | −0.256357 | − | 0.115565i | ||||
\(397\) | −355.449 | −0.895338 | −0.447669 | − | 0.894199i | \(-0.647746\pi\) | ||||
−0.447669 | + | 0.894199i | \(0.647746\pi\) | |||||||
\(398\) | 273.088 | + | 422.661i | 0.686151 | + | 1.06196i | ||||
\(399\) | 7.28180i | 0.0182501i | ||||||||
\(400\) | −52.9767 | − | 59.9455i | −0.132442 | − | 0.149864i | ||||
\(401\) | −542.927 | −1.35393 | −0.676966 | − | 0.736014i | \(-0.736706\pi\) | ||||
−0.676966 | + | 0.736014i | \(0.736706\pi\) | |||||||
\(402\) | −202.910 | + | 131.103i | −0.504751 | + | 0.326128i | ||||
\(403\) | 1393.27i | 3.45724i | ||||||||
\(404\) | −6.01792 | + | 13.3495i | −0.0148958 | + | 0.0330433i | ||||
\(405\) | 20.1246 | 0.0496904 | ||||||||
\(406\) | 23.0977 | + | 35.7485i | 0.0568908 | + | 0.0880505i | ||||
\(407\) | − | 49.9950i | − | 0.122838i | ||||||
\(408\) | 54.4941 | − | 8.24285i | 0.133564 | − | 0.0202031i | ||||
\(409\) | −108.497 | −0.265273 | −0.132636 | − | 0.991165i | \(-0.542344\pi\) | ||||
−0.132636 | + | 0.991165i | \(0.542344\pi\) | |||||||
\(410\) | 150.549 | − | 97.2718i | 0.367192 | − | 0.237248i | ||||
\(411\) | − | 239.295i | − | 0.582227i | ||||||
\(412\) | −552.156 | − | 248.910i | −1.34018 | − | 0.604151i | ||||
\(413\) | −21.7156 | −0.0525801 | ||||||||
\(414\) | −104.455 | − | 161.666i | −0.252307 | − | 0.390499i | ||||
\(415\) | 290.486i | 0.699966i | ||||||||
\(416\) | 724.431 | + | 203.141i | 1.74142 | + | 0.488320i | ||||
\(417\) | 51.8884 | 0.124433 | ||||||||
\(418\) | 109.861 | − | 70.9828i | 0.262825 | − | 0.169815i | ||||
\(419\) | − | 172.176i | − | 0.410921i | −0.978665 | − | 0.205460i | \(-0.934131\pi\) | ||
0.978665 | − | 0.205460i | \(-0.0658691\pi\) | |||||||
\(420\) | −3.79799 | + | 8.42505i | −0.00904283 | + | 0.0200597i | ||||
\(421\) | 478.522 | 1.13663 | 0.568316 | − | 0.822810i | \(-0.307595\pi\) | ||||
0.568316 | + | 0.822810i | \(0.307595\pi\) | |||||||
\(422\) | 247.688 | + | 383.350i | 0.586940 | + | 0.908412i | ||||
\(423\) | 222.039i | 0.524915i | ||||||||
\(424\) | 3.05250 | + | 20.1803i | 0.00719929 | + | 0.0475950i | ||||
\(425\) | 19.8875 | 0.0467942 | ||||||||
\(426\) | 172.298 | − | 111.325i | 0.404456 | − | 0.261326i | ||||
\(427\) | − | 5.20912i | − | 0.0121993i | ||||||
\(428\) | −301.972 | − | 136.128i | −0.705541 | − | 0.318056i | ||||
\(429\) | 377.898 | 0.880882 | ||||||||
\(430\) | 87.6528 | + | 135.661i | 0.203844 | + | 0.315491i | ||||
\(431\) | − | 290.722i | − | 0.674530i | −0.941410 | − | 0.337265i | \(-0.890498\pi\) | ||
0.941410 | − | 0.337265i | \(-0.109502\pi\) | |||||||
\(432\) | −62.2972 | + | 55.0550i | −0.144207 | + | 0.127442i | ||||
\(433\) | 53.7726 | 0.124186 | 0.0620931 | − | 0.998070i | \(-0.480222\pi\) | ||||
0.0620931 | + | 0.998070i | \(0.480222\pi\) | |||||||
\(434\) | 59.3832 | − | 38.3684i | 0.136828 | − | 0.0884065i | ||||
\(435\) | 138.163i | 0.317615i | ||||||||
\(436\) | −12.1127 | + | 26.8694i | −0.0277813 | + | 0.0616271i | ||||
\(437\) | 226.081 | 0.517347 | ||||||||
\(438\) | −156.039 | − | 241.503i | −0.356253 | − | 0.551376i | ||||
\(439\) | 328.657i | 0.748650i | 0.927298 | + | 0.374325i | \(0.122126\pi\) | ||||
−0.927298 | + | 0.374325i | \(0.877874\pi\) | |||||||
\(440\) | 164.132 | − | 24.8268i | 0.373027 | − | 0.0564246i | ||||
\(441\) | −145.932 | −0.330913 | ||||||||
\(442\) | −157.097 | + | 101.503i | −0.355424 | + | 0.229645i | ||||
\(443\) | 428.910i | 0.968194i | 0.875014 | + | 0.484097i | \(0.160852\pi\) | ||||
−0.875014 | + | 0.484097i | \(0.839148\pi\) | |||||||
\(444\) | −34.0286 | − | 15.3400i | −0.0766410 | − | 0.0345496i | ||||
\(445\) | −291.731 | −0.655575 | ||||||||
\(446\) | −93.2942 | − | 144.392i | −0.209180 | − | 0.323750i | ||||
\(447\) | − | 82.0685i | − | 0.183599i | ||||||
\(448\) | −11.2915 | − | 36.4706i | −0.0252043 | − | 0.0814075i | ||||
\(449\) | 409.229 | 0.911423 | 0.455711 | − | 0.890128i | \(-0.349385\pi\) | ||||
0.455711 | + | 0.890128i | \(0.349385\pi\) | |||||||
\(450\) | −25.1979 | + | 16.2808i | −0.0559954 | + | 0.0361795i | ||||
\(451\) | 371.919i | 0.824654i | ||||||||
\(452\) | 106.913 | − | 237.164i | 0.236533 | − | 0.524698i | ||||
\(453\) | −189.839 | −0.419071 | ||||||||
\(454\) | 306.466 | + | 474.321i | 0.675036 | + | 1.04476i | ||||
\(455\) | − | 31.3623i | − | 0.0689281i | ||||||
\(456\) | −14.6051 | − | 96.5555i | −0.0320288 | − | 0.211745i | ||||
\(457\) | 768.561 | 1.68175 | 0.840876 | − | 0.541228i | \(-0.182040\pi\) | ||||
0.840876 | + | 0.541228i | \(0.182040\pi\) | |||||||
\(458\) | 232.262 | − | 150.068i | 0.507123 | − | 0.327660i | ||||
\(459\) | − | 20.6677i | − | 0.0450278i | ||||||
\(460\) | 261.576 | + | 117.918i | 0.568643 | + | 0.256343i | ||||
\(461\) | −316.563 | −0.686687 | −0.343343 | − | 0.939210i | \(-0.611559\pi\) | ||||
−0.343343 | + | 0.939210i | \(0.611559\pi\) | |||||||
\(462\) | −10.4067 | − | 16.1066i | −0.0225254 | − | 0.0348628i | ||||
\(463\) | − | 491.208i | − | 1.06093i | −0.847708 | − | 0.530463i | \(-0.822018\pi\) | ||
0.847708 | − | 0.530463i | \(-0.177982\pi\) | |||||||
\(464\) | −377.972 | − | 427.692i | −0.814596 | − | 0.921751i | ||||
\(465\) | 229.507 | 0.493564 | ||||||||
\(466\) | −0.878466 | + | 0.567591i | −0.00188512 | + | 0.00121801i | ||||
\(467\) | − | 410.393i | − | 0.878785i | −0.898295 | − | 0.439393i | \(-0.855194\pi\) | ||
0.898295 | − | 0.439393i | \(-0.144806\pi\) | |||||||
\(468\) | 115.951 | − | 257.213i | 0.247758 | − | 0.549600i | ||||
\(469\) | −41.6014 | −0.0887024 | ||||||||
\(470\) | −179.629 | − | 278.014i | −0.382190 | − | 0.591520i | ||||
\(471\) | − | 307.591i | − | 0.653060i | ||||||
\(472\) | 287.945 | − | 43.5550i | 0.610054 | − | 0.0922776i | ||||
\(473\) | −335.141 | −0.708542 | ||||||||
\(474\) | −191.657 | + | 123.833i | −0.404341 | + | 0.261251i | ||||
\(475\) | − | 35.2378i | − | 0.0741848i | ||||||
\(476\) | 8.65243 | + | 3.90049i | 0.0181774 | + | 0.00819431i | ||||
\(477\) | 7.65369 | 0.0160455 | ||||||||
\(478\) | 79.9851 | + | 123.794i | 0.167333 | + | 0.258983i | ||||
\(479\) | − | 198.918i | − | 0.415277i | −0.978206 | − | 0.207638i | \(-0.933422\pi\) | ||
0.978206 | − | 0.207638i | \(-0.0665778\pi\) | |||||||
\(480\) | 33.4626 | − | 119.333i | 0.0697137 | − | 0.248609i | ||||
\(481\) | 126.672 | 0.263351 | ||||||||
\(482\) | 52.6981 | − | 34.0491i | 0.109332 | − | 0.0706413i | ||||
\(483\) | − | 33.1455i | − | 0.0686242i | ||||||
\(484\) | 57.3524 | − | 127.224i | 0.118497 | − | 0.262860i | ||||
\(485\) | 208.203 | 0.429285 | ||||||||
\(486\) | 16.9195 | + | 26.1865i | 0.0348138 | + | 0.0538816i | ||||
\(487\) | 204.762i | 0.420456i | 0.977652 | + | 0.210228i | \(0.0674206\pi\) | ||||
−0.977652 | + | 0.210228i | \(0.932579\pi\) | |||||||
\(488\) | 10.4479 | + | 69.0721i | 0.0214097 | + | 0.141541i | ||||
\(489\) | 167.797 | 0.343144 | ||||||||
\(490\) | 182.721 | − | 118.059i | 0.372901 | − | 0.240937i | ||||
\(491\) | − | 788.598i | − | 1.60611i | −0.595908 | − | 0.803053i | \(-0.703208\pi\) | ||
0.595908 | − | 0.803053i | \(-0.296792\pi\) | |||||||
\(492\) | 253.143 | + | 114.116i | 0.514519 | + | 0.231944i | ||||
\(493\) | 141.891 | 0.287812 | ||||||||
\(494\) | 179.848 | + | 278.353i | 0.364066 | + | 0.563468i | ||||
\(495\) | − | 62.2496i | − | 0.125757i | ||||||
\(496\) | −710.456 | + | 627.864i | −1.43237 | + | 1.26586i | ||||
\(497\) | 35.3253 | 0.0710771 | ||||||||
\(498\) | −377.985 | + | 244.222i | −0.759006 | + | 0.490406i | ||||
\(499\) | − | 740.385i | − | 1.48374i | −0.670545 | − | 0.741869i | \(-0.733940\pi\) | ||
0.670545 | − | 0.741869i | \(-0.266060\pi\) | |||||||
\(500\) | 18.3791 | − | 40.7702i | 0.0367582 | − | 0.0815404i | ||||
\(501\) | −264.319 | −0.527583 | ||||||||
\(502\) | 85.4717 | + | 132.285i | 0.170262 | + | 0.263517i | ||||
\(503\) | − | 70.8800i | − | 0.140914i | −0.997515 | − | 0.0704572i | \(-0.977554\pi\) | ||
0.997515 | − | 0.0704572i | \(-0.0224458\pi\) | |||||||
\(504\) | −14.1559 | + | 2.14124i | −0.0280871 | + | 0.00424850i | ||||
\(505\) | −8.18582 | −0.0162095 | ||||||||
\(506\) | −500.068 | + | 323.102i | −0.988277 | + | 0.638541i | ||||
\(507\) | 664.760i | 1.31116i | ||||||||
\(508\) | −508.588 | − | 229.270i | −1.00116 | − | 0.451318i | ||||
\(509\) | 522.642 | 1.02680 | 0.513400 | − | 0.858149i | \(-0.328386\pi\) | ||||
0.513400 | + | 0.858149i | \(0.328386\pi\) | |||||||
\(510\) | 16.7202 | + | 25.8780i | 0.0327847 | + | 0.0507411i | ||||
\(511\) | − | 49.5139i | − | 0.0968961i | ||||||
\(512\) | 222.873 | + | 460.946i | 0.435299 | + | 0.900286i | ||||
\(513\) | −36.6202 | −0.0713844 | ||||||||
\(514\) | 409.809 | − | 264.784i | 0.797293 | − | 0.515144i | ||||
\(515\) | − | 338.578i | − | 0.657433i | ||||||
\(516\) | −102.831 | + | 228.110i | −0.199286 | + | 0.442074i | ||||
\(517\) | 686.813 | 1.32846 | ||||||||
\(518\) | −3.48834 | − | 5.39894i | −0.00673425 | − | 0.0104227i | ||||
\(519\) | 269.807i | 0.519859i | ||||||||
\(520\) | 62.9034 | + | 415.859i | 0.120968 | + | 0.799729i | ||||
\(521\) | 304.082 | 0.583650 | 0.291825 | − | 0.956472i | \(-0.405738\pi\) | ||||
0.291825 | + | 0.956472i | \(0.405738\pi\) | |||||||
\(522\) | −179.779 | + | 116.158i | −0.344405 | + | 0.222525i | ||||
\(523\) | 174.416i | 0.333491i | 0.986000 | + | 0.166746i | \(0.0533259\pi\) | ||||
−0.986000 | + | 0.166746i | \(0.946674\pi\) | |||||||
\(524\) | 231.507 | + | 104.362i | 0.441806 | + | 0.199165i | ||||
\(525\) | −5.16618 | −0.00984035 | ||||||||
\(526\) | 111.509 | + | 172.584i | 0.211995 | + | 0.328106i | ||||
\(527\) | − | 235.701i | − | 0.447251i | ||||||
\(528\) | 170.297 | + | 192.698i | 0.322532 | + | 0.364959i | ||||
\(529\) | −500.081 | −0.945333 | ||||||||
\(530\) | −9.58315 | + | 6.19182i | −0.0180814 | + | 0.0116827i | ||||
\(531\) | − | 109.208i | − | 0.205664i | ||||||
\(532\) | 6.91109 | − | 15.3308i | 0.0129908 | − | 0.0288174i | ||||
\(533\) | −942.327 | −1.76797 | ||||||||
\(534\) | −245.269 | − | 379.605i | −0.459305 | − | 0.710871i | ||||
\(535\) | − | 185.167i | − | 0.346106i | ||||||
\(536\) | 551.628 | − | 83.4401i | 1.02916 | − | 0.155672i | ||||
\(537\) | 218.240 | 0.406405 | ||||||||
\(538\) | −207.708 | + | 134.204i | −0.386075 | + | 0.249449i | ||||
\(539\) | 451.399i | 0.837476i | ||||||||
\(540\) | −42.3696 | − | 19.1001i | −0.0784623 | − | 0.0353706i | ||||
\(541\) | −262.199 | −0.484655 | −0.242328 | − | 0.970194i | \(-0.577911\pi\) | ||||
−0.242328 | + | 0.970194i | \(0.577911\pi\) | |||||||
\(542\) | −360.750 | − | 558.337i | −0.665591 | − | 1.03014i | ||||
\(543\) | − | 600.545i | − | 1.10598i | ||||||
\(544\) | −122.553 | − | 34.3657i | −0.225281 | − | 0.0631722i | ||||
\(545\) | −16.4761 | −0.0302314 | ||||||||
\(546\) | 40.8091 | − | 26.3674i | 0.0747420 | − | 0.0482920i | ||||
\(547\) | − | 146.179i | − | 0.267237i | −0.991033 | − | 0.133619i | \(-0.957340\pi\) | ||
0.991033 | − | 0.133619i | \(-0.0426598\pi\) | |||||||
\(548\) | −227.113 | + | 503.804i | −0.414440 | + | 0.919350i | ||||
\(549\) | 26.1967 | 0.0477171 | ||||||||
\(550\) | 50.3599 | + | 77.9425i | 0.0915634 | + | 0.141714i | ||||
\(551\) | − | 251.411i | − | 0.456281i | ||||||
\(552\) | 66.4800 | + | 439.504i | 0.120435 | + | 0.796203i | ||||
\(553\) | −39.2944 | −0.0710568 | ||||||||
\(554\) | −211.522 | + | 136.668i | −0.381809 | + | 0.246693i | ||||
\(555\) | − | 20.8661i | − | 0.0375966i | ||||||
\(556\) | −109.244 | − | 49.2468i | −0.196482 | − | 0.0885734i | ||||
\(557\) | 187.700 | 0.336984 | 0.168492 | − | 0.985703i | \(-0.446110\pi\) | ||||
0.168492 | + | 0.985703i | \(0.446110\pi\) | |||||||
\(558\) | 192.955 | + | 298.638i | 0.345797 | + | 0.535194i | ||||
\(559\) | − | 849.142i | − | 1.51904i | ||||||
\(560\) | 15.9923 | − | 14.1332i | 0.0285577 | − | 0.0252378i | ||||
\(561\) | −63.9296 | −0.113957 | ||||||||
\(562\) | 88.2982 | − | 57.0509i | 0.157114 | − | 0.101514i | ||||
\(563\) | 447.848i | 0.795467i | 0.917501 | + | 0.397734i | \(0.130203\pi\) | ||||
−0.917501 | + | 0.397734i | \(0.869797\pi\) | |||||||
\(564\) | 210.736 | − | 467.473i | 0.373645 | − | 0.828853i | ||||
\(565\) | 145.427 | 0.257393 | ||||||||
\(566\) | −216.305 | − | 334.777i | −0.382164 | − | 0.591479i | ||||
\(567\) | 5.36886i | 0.00946888i | ||||||||
\(568\) | −468.408 | + | 70.8520i | −0.824662 | + | 0.124740i | ||||
\(569\) | 1078.91 | 1.89615 | 0.948077 | − | 0.318042i | \(-0.103025\pi\) | ||||
0.948077 | + | 0.318042i | \(0.103025\pi\) | |||||||
\(570\) | 45.8520 | − | 29.6257i | 0.0804421 | − | 0.0519749i | ||||
\(571\) | 936.324i | 1.63980i | 0.572509 | + | 0.819899i | \(0.305970\pi\) | ||||
−0.572509 | + | 0.819899i | \(0.694030\pi\) | |||||||
\(572\) | −795.613 | − | 358.660i | −1.39093 | − | 0.627028i | ||||
\(573\) | −230.638 | −0.402510 | ||||||||
\(574\) | 25.9502 | + | 40.1634i | 0.0452095 | + | 0.0699711i | ||||
\(575\) | 160.396i | 0.278950i | ||||||||
\(576\) | 183.411 | − | 56.7851i | 0.318421 | − | 0.0985853i | ||||
\(577\) | −544.832 | −0.944250 | −0.472125 | − | 0.881532i | \(-0.656513\pi\) | ||||
−0.472125 | + | 0.881532i | \(0.656513\pi\) | |||||||
\(578\) | −458.904 | + | 296.505i | −0.793951 | + | 0.512985i | ||||
\(579\) | − | 235.986i | − | 0.407575i | ||||||
\(580\) | 131.129 | − | 290.883i | 0.226084 | − | 0.501522i | ||||
\(581\) | −77.4960 | −0.133384 | ||||||||
\(582\) | 175.044 | + | 270.917i | 0.300763 | + | 0.465494i | ||||
\(583\) | − | 23.6745i | − | 0.0406080i | ||||||
\(584\) | 99.3101 | + | 656.547i | 0.170052 | + | 1.12422i | ||||
\(585\) | 157.721 | 0.269609 | ||||||||
\(586\) | 171.616 | − | 110.884i | 0.292861 | − | 0.189222i | ||||
\(587\) | 337.889i | 0.575619i | 0.957688 | + | 0.287810i | \(0.0929271\pi\) | ||||
−0.957688 | + | 0.287810i | \(0.907073\pi\) | |||||||
\(588\) | 307.241 | + | 138.503i | 0.522519 | + | 0.235550i | ||||
\(589\) | −417.628 | −0.709045 | ||||||||
\(590\) | 88.3490 | + | 136.739i | 0.149744 | + | 0.231760i | ||||
\(591\) | 129.721i | 0.219494i | ||||||||
\(592\) | 57.0836 | + | 64.5926i | 0.0964249 | + | 0.109109i | ||||
\(593\) | 567.269 | 0.956608 | 0.478304 | − | 0.878194i | \(-0.341252\pi\) | ||||
0.478304 | + | 0.878194i | \(0.341252\pi\) | |||||||
\(594\) | 81.0002 | − | 52.3355i | 0.136364 | − | 0.0881069i | ||||
\(595\) | 5.30561i | 0.00891699i | ||||||||
\(596\) | −77.8906 | + | 172.784i | −0.130689 | + | 0.289906i | ||||
\(597\) | −435.792 | −0.729969 | ||||||||
\(598\) | −818.640 | − | 1267.02i | −1.36896 | − | 2.11876i | ||||
\(599\) | 762.966i | 1.27373i | 0.770974 | + | 0.636867i | \(0.219770\pi\) | ||||
−0.770974 | + | 0.636867i | \(0.780230\pi\) | |||||||
\(600\) | 68.5028 | − | 10.3618i | 0.114171 | − | 0.0172697i | ||||
\(601\) | −790.102 | −1.31464 | −0.657322 | − | 0.753609i | \(-0.728311\pi\) | ||||
−0.657322 | + | 0.753609i | \(0.728311\pi\) | |||||||
\(602\) | −36.1917 | + | 23.3841i | −0.0601192 | + | 0.0388440i | ||||
\(603\) | − | 209.214i | − | 0.346955i | ||||||
\(604\) | 399.680 | + | 180.175i | 0.661722 | + | 0.298302i | ||||
\(605\) | 78.0132 | 0.128947 | ||||||||
\(606\) | −6.88212 | − | 10.6515i | −0.0113566 | − | 0.0175768i | ||||
\(607\) | − | 522.994i | − | 0.861605i | −0.902446 | − | 0.430802i | \(-0.858231\pi\) | ||
0.902446 | − | 0.430802i | \(-0.141769\pi\) | |||||||
\(608\) | −60.8909 | + | 217.146i | −0.100150 | + | 0.357148i | ||||
\(609\) | −36.8591 | −0.0605240 | ||||||||
\(610\) | −32.8008 | + | 21.1931i | −0.0537717 | + | 0.0347428i | ||||
\(611\) | 1740.17i | 2.84807i | ||||||||
\(612\) | −19.6156 | + | 43.5131i | −0.0320516 | + | 0.0710999i | ||||
\(613\) | 1026.91 | 1.67522 | 0.837609 | − | 0.546270i | \(-0.183953\pi\) | ||||
0.837609 | + | 0.546270i | \(0.183953\pi\) | |||||||
\(614\) | −356.431 | − | 551.652i | −0.580506 | − | 0.898455i | ||||
\(615\) | 155.226i | 0.252399i | ||||||||
\(616\) | 6.62332 | + | 43.7872i | 0.0107521 | + | 0.0710831i | ||||
\(617\) | −479.223 | −0.776698 | −0.388349 | − | 0.921512i | \(-0.626954\pi\) | ||||
−0.388349 | + | 0.921512i | \(0.626954\pi\) | |||||||
\(618\) | 440.563 | − | 284.655i | 0.712886 | − | 0.460607i | ||||
\(619\) | − | 507.654i | − | 0.820119i | −0.912059 | − | 0.410059i | \(-0.865508\pi\) | ||
0.912059 | − | 0.410059i | \(-0.134492\pi\) | |||||||
\(620\) | −483.196 | − | 217.823i | −0.779348 | − | 0.351328i | ||||
\(621\) | 166.689 | 0.268420 | ||||||||
\(622\) | −103.587 | − | 160.322i | −0.166538 | − | 0.257753i | ||||
\(623\) | − | 77.8282i | − | 0.124925i | ||||||
\(624\) | −488.237 | + | 431.479i | −0.782432 | + | 0.691473i | ||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 924.609 | − | 597.405i | 1.47701 | − | 0.954321i | ||||
\(627\) | 113.274i | 0.180660i | ||||||||
\(628\) | −291.932 | + | 647.591i | −0.464860 | + | 1.03120i | ||||
\(629\) | −21.4293 | −0.0340688 | ||||||||
\(630\) | −4.34340 | − | 6.72232i | −0.00689428 | − | 0.0106703i | ||||
\(631\) | − | 460.186i | − | 0.729297i | −0.931145 | − | 0.364648i | \(-0.881189\pi\) | ||
0.931145 | − | 0.364648i | \(-0.118811\pi\) | |||||||
\(632\) | 521.037 | − | 78.8128i | 0.824426 | − | 0.124704i | ||||
\(633\) | −395.259 | −0.624423 | ||||||||
\(634\) | 738.122 | − | 476.912i | 1.16423 | − | 0.752228i | ||||
\(635\) | − | 311.862i | − | 0.491122i | ||||||
\(636\) | −16.1138 | − | 7.26405i | −0.0253362 | − | 0.0114215i | ||||
\(637\) | −1143.71 | −1.79546 | ||||||||
\(638\) | 359.302 | + | 556.095i | 0.563169 | + | 0.871622i | ||||
\(639\) | 177.651i | 0.278014i | ||||||||
\(640\) | −183.708 | + | 219.479i | −0.287045 | + | 0.342937i | ||||
\(641\) | 250.774 | 0.391223 | 0.195612 | − | 0.980681i | \(-0.437331\pi\) | ||||
0.195612 | + | 0.980681i | \(0.437331\pi\) | |||||||
\(642\) | 240.942 | − | 155.677i | 0.375299 | − | 0.242487i | ||||
\(643\) | − | 590.355i | − | 0.918126i | −0.888404 | − | 0.459063i | \(-0.848185\pi\) | ||
0.888404 | − | 0.459063i | \(-0.151815\pi\) | |||||||
\(644\) | −31.4581 | + | 69.7834i | −0.0488480 | + | 0.108359i | ||||
\(645\) | −139.876 | −0.216862 | ||||||||
\(646\) | −30.4252 | − | 47.0894i | −0.0470979 | − | 0.0728939i | ||||
\(647\) | − | 319.341i | − | 0.493572i | −0.969070 | − | 0.246786i | \(-0.920626\pi\) | ||
0.969070 | − | 0.246786i | \(-0.0793744\pi\) | |||||||
\(648\) | −10.7683 | − | 71.1902i | −0.0166178 | − | 0.109861i | ||||
\(649\) | −337.803 | −0.520497 | ||||||||
\(650\) | −197.482 | + | 127.596i | −0.303818 | + | 0.196302i | ||||
\(651\) | 61.2280i | 0.0940523i | ||||||||
\(652\) | −353.274 | − | 159.255i | −0.541832 | − | 0.244256i | ||||
\(653\) | 88.5949 | 0.135674 | 0.0678369 | − | 0.997696i | \(-0.478390\pi\) | ||||
0.0678369 | + | 0.997696i | \(0.478390\pi\) | |||||||
\(654\) | −13.8521 | − | 21.4390i | −0.0211806 | − | 0.0327814i | ||||
\(655\) | 141.958i | 0.216730i | ||||||||
\(656\) | −424.652 | − | 480.512i | −0.647335 | − | 0.732488i | ||||
\(657\) | 249.006 | 0.379004 | ||||||||
\(658\) | 74.1688 | − | 47.9216i | 0.112719 | − | 0.0728292i | ||||
\(659\) | 758.423i | 1.15087i | 0.817847 | + | 0.575435i | \(0.195167\pi\) | ||||
−0.817847 | + | 0.575435i | \(0.804833\pi\) | |||||||
\(660\) | −59.0806 | + | 131.058i | −0.0895161 | + | 0.198573i | ||||
\(661\) | 527.327 | 0.797771 | 0.398885 | − | 0.917001i | \(-0.369397\pi\) | ||||
0.398885 | + | 0.917001i | \(0.369397\pi\) | |||||||
\(662\) | −520.900 | − | 806.203i | −0.786859 | − | 1.21783i | ||||
\(663\) | − | 161.978i | − | 0.244310i | ||||||
\(664\) | 1027.59 | − | 155.434i | 1.54757 | − | 0.234087i | ||||
\(665\) | 9.40076 | 0.0141365 | ||||||||
\(666\) | 27.1513 | − | 17.5429i | 0.0407677 | − | 0.0263407i | ||||
\(667\) | 1144.38i | 1.71571i | ||||||||
\(668\) | 556.488 | + | 250.863i | 0.833066 | + | 0.375544i | ||||
\(669\) | 148.878 | 0.222538 | ||||||||
\(670\) | 169.254 | + | 261.956i | 0.252617 | + | 0.390978i | ||||
\(671\) | − | 81.0318i | − | 0.120763i | ||||||
\(672\) | 31.8356 | + | 8.92717i | 0.0473744 | + | 0.0132845i | ||||
\(673\) | 120.657 | 0.179283 | 0.0896415 | − | 0.995974i | \(-0.471428\pi\) | ||||
0.0896415 | + | 0.995974i | \(0.471428\pi\) | |||||||
\(674\) | 98.8493 | − | 63.8681i | 0.146661 | − | 0.0947598i | ||||
\(675\) | − | 25.9808i | − | 0.0384900i | ||||||
\(676\) | 630.918 | − | 1399.56i | 0.933311 | − | 2.07036i | ||||
\(677\) | −219.196 | −0.323776 | −0.161888 | − | 0.986809i | \(-0.551758\pi\) | ||||
−0.161888 | + | 0.986809i | \(0.551758\pi\) | |||||||
\(678\) | 122.266 | + | 189.232i | 0.180333 | + | 0.279103i | ||||
\(679\) | 55.5446i | 0.0818035i | ||||||||
\(680\) | −10.6415 | − | 70.3516i | −0.0156492 | − | 0.103458i | ||||
\(681\) | −489.057 | −0.718145 | ||||||||
\(682\) | 923.751 | − | 596.850i | 1.35447 | − | 0.875146i | ||||
\(683\) | − | 205.502i | − | 0.300881i | −0.988619 | − | 0.150441i | \(-0.951931\pi\) | ||
0.988619 | − | 0.150441i | \(-0.0480693\pi\) | |||||||
\(684\) | 77.0988 | + | 34.7559i | 0.112718 | + | 0.0508128i | ||||
\(685\) | −308.929 | −0.450991 | ||||||||
\(686\) | 63.2222 | + | 97.8496i | 0.0921606 | + | 0.142638i | ||||
\(687\) | 239.478i | 0.348585i | ||||||||
\(688\) | 432.995 | − | 382.659i | 0.629354 | − | 0.556190i | ||||
\(689\) | 59.9837 | 0.0870591 | ||||||||
\(690\) | −208.710 | + | 134.851i | −0.302479 | + | 0.195436i | ||||
\(691\) | − | 109.536i | − | 0.158519i | −0.996854 | − | 0.0792593i | \(-0.974744\pi\) | ||
0.996854 | − | 0.0792593i | \(-0.0252555\pi\) | |||||||
\(692\) | 256.071 | − | 568.042i | 0.370045 | − | 0.820869i | ||||
\(693\) | 16.6070 | 0.0239639 | ||||||||
\(694\) | 13.1857 | + | 20.4077i | 0.0189996 | + | 0.0294059i | ||||
\(695\) | − | 66.9876i | − | 0.0963850i | ||||||
\(696\) | 488.746 | − | 73.9284i | 0.702221 | − | 0.106219i | ||||
\(697\) | 159.415 | 0.228716 | ||||||||
\(698\) | −51.9543 | + | 33.5685i | −0.0744331 | + | 0.0480924i | ||||
\(699\) | − | 0.905758i | − | 0.00129579i | ||||||
\(700\) | 10.8767 | + | 4.90318i | 0.0155381 | + | 0.00700455i | ||||
\(701\) | 168.847 | 0.240865 | 0.120433 | − | 0.992721i | \(-0.461572\pi\) | ||||
0.120433 | + | 0.992721i | \(0.461572\pi\) | |||||||
\(702\) | 132.602 | + | 205.229i | 0.188892 | + | 0.292349i | ||||
\(703\) | 37.9695i | 0.0540106i | ||||||||
\(704\) | −175.648 | − | 567.327i | −0.249500 | − | 0.805863i | ||||
\(705\) | 286.651 | 0.406598 | ||||||||
\(706\) | −483.909 | + | 312.661i | −0.685424 | + | 0.442863i | ||||
\(707\) | − | 2.18382i | − | 0.00308885i | ||||||
\(708\) | −103.648 | + | 229.922i | −0.146396 | + | 0.324749i | ||||
\(709\) | −554.846 | −0.782576 | −0.391288 | − | 0.920268i | \(-0.627970\pi\) | ||||
−0.391288 | + | 0.920268i | \(0.627970\pi\) | |||||||
\(710\) | −143.720 | − | 222.436i | −0.202422 | − | 0.313290i | ||||
\(711\) | − | 197.612i | − | 0.277935i | ||||||
\(712\) | 156.100 | + | 1031.99i | 0.219242 | + | 1.44942i | ||||
\(713\) | 1900.97 | 2.66616 | ||||||||
\(714\) | −6.90374 | + | 4.46062i | −0.00966911 | + | 0.00624737i | ||||
\(715\) | − | 487.864i | − | 0.682328i | ||||||
\(716\) | −459.474 | − | 207.130i | −0.641723 | − | 0.289287i | ||||
\(717\) | −127.640 | −0.178019 | ||||||||
\(718\) | 720.600 | + | 1115.28i | 1.00362 | + | 1.55331i | ||||
\(719\) | 377.485i | 0.525014i | 0.964930 | + | 0.262507i | \(0.0845494\pi\) | ||||
−0.964930 | + | 0.262507i | \(0.915451\pi\) | |||||||
\(720\) | 71.0758 | + | 80.4254i | 0.0987163 | + | 0.111702i | ||||
\(721\) | 90.3261 | 0.125279 | ||||||||
\(722\) | 522.995 | − | 337.915i | 0.724369 | − | 0.468027i | ||||
\(723\) | 54.3353i | 0.0751525i | ||||||||
\(724\) | −569.972 | + | 1264.37i | −0.787255 | + | 1.74636i | ||||
\(725\) | 178.367 | 0.246024 | ||||||||
\(726\) | 65.5885 | + | 101.512i | 0.0903423 | + | 0.139824i | ||||
\(727\) | 173.183i | 0.238216i | 0.992881 | + | 0.119108i | \(0.0380035\pi\) | ||||
−0.992881 | + | 0.119108i | \(0.961997\pi\) | |||||||
\(728\) | −110.943 | + | 16.7814i | −0.152394 | + | 0.0230514i | ||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | −311.779 | + | 201.445i | −0.427094 | + | 0.275952i | ||||
\(731\) | 143.651i | 0.196513i | ||||||||
\(732\) | −55.1536 | − | 24.8631i | −0.0753464 | − | 0.0339659i | ||||
\(733\) | 278.722 | 0.380249 | 0.190124 | − | 0.981760i | \(-0.439111\pi\) | ||||
0.190124 | + | 0.981760i | \(0.439111\pi\) | |||||||
\(734\) | 6.60489 | + | 10.2225i | 0.00899849 | + | 0.0139270i | ||||
\(735\) | 188.398i | 0.256324i | ||||||||
\(736\) | 277.165 | − | 988.412i | 0.376583 | − | 1.34295i | ||||
\(737\) | −647.142 | −0.878075 | ||||||||
\(738\) | −201.982 | + | 130.504i | −0.273688 | + | 0.176834i | ||||
\(739\) | 521.363i | 0.705498i | 0.935718 | + | 0.352749i | \(0.114753\pi\) | ||||
−0.935718 | + | 0.352749i | \(0.885247\pi\) | |||||||
\(740\) | −19.8039 | + | 43.9308i | −0.0267620 | + | 0.0593659i | ||||
\(741\) | −287.001 | −0.387315 | ||||||||
\(742\) | −1.65186 | − | 2.55660i | −0.00222622 | − | 0.00344555i | ||||
\(743\) | − | 1277.93i | − | 1.71996i | −0.510326 | − | 0.859981i | \(-0.670475\pi\) | ||
0.510326 | − | 0.859981i | \(-0.329525\pi\) | |||||||
\(744\) | −122.805 | − | 811.874i | −0.165061 | − | 1.09123i | ||||
\(745\) | −105.950 | −0.142215 | ||||||||
\(746\) | −343.936 | + | 222.223i | −0.461041 | + | 0.297886i | ||||
\(747\) | − | 389.728i | − | 0.521724i | ||||||
\(748\) | 134.595 | + | 60.6751i | 0.179940 | + | 0.0811164i | ||||
\(749\) | 49.3989 | 0.0659532 | ||||||||
\(750\) | 21.0184 | + | 32.5304i | 0.0280245 | + | 0.0433739i | ||||
\(751\) | 1165.31i | 1.55168i | 0.630930 | + | 0.775840i | \(0.282673\pi\) | ||||
−0.630930 | + | 0.775840i | \(0.717327\pi\) | |||||||
\(752\) | −887.350 | + | 784.194i | −1.17999 | + | 1.04281i | ||||
\(753\) | −136.395 | −0.181136 | ||||||||
\(754\) | −1408.97 | + | 910.359i | −1.86866 | + | 1.20737i | ||||
\(755\) | 245.081i | 0.324611i | ||||||||
\(756\) | 5.09554 | − | 11.3034i | 0.00674013 | − | 0.0149516i | ||||
\(757\) | 1063.75 | 1.40522 | 0.702611 | − | 0.711574i | \(-0.252017\pi\) | ||||
0.702611 | + | 0.711574i | \(0.252017\pi\) | |||||||
\(758\) | −436.685 | − | 675.861i | −0.576101 | − | 0.891638i | ||||
\(759\) | − | 515.604i | − | 0.679320i | ||||||
\(760\) | −124.653 | + | 18.8551i | −0.164017 | + | 0.0248094i | ||||
\(761\) | −677.847 | −0.890732 | −0.445366 | − | 0.895349i | \(-0.646926\pi\) | ||||
−0.445366 | + | 0.895349i | \(0.646926\pi\) | |||||||
\(762\) | 405.800 | − | 262.194i | 0.532546 | − | 0.344087i | ||||
\(763\) | − | 4.39551i | − | 0.00576083i | ||||||
\(764\) | 485.577 | + | 218.897i | 0.635572 | + | 0.286514i | ||||
\(765\) | −26.6819 | −0.0348784 | ||||||||
\(766\) | −360.078 | − | 557.296i | −0.470076 | − | 0.727541i | ||||
\(767\) | − | 855.887i | − | 1.11589i | ||||||
\(768\) | −440.040 | − | 54.5201i | −0.572969 | − | 0.0709898i | ||||
\(769\) | −1289.59 | −1.67697 | −0.838486 | − | 0.544922i | \(-0.816559\pi\) | ||||
−0.838486 | + | 0.544922i | \(0.816559\pi\) | |||||||
\(770\) | −20.7935 | + | 13.4350i | −0.0270046 | + | 0.0174481i | ||||
\(771\) | 422.540i | 0.548042i | ||||||||
\(772\) | −223.972 | + | 496.836i | −0.290119 | + | 0.643570i | ||||
\(773\) | −750.339 | −0.970684 | −0.485342 | − | 0.874324i | \(-0.661305\pi\) | ||||
−0.485342 | + | 0.874324i | \(0.661305\pi\) | |||||||
\(774\) | −117.599 | − | 182.008i | −0.151936 | − | 0.235153i | ||||
\(775\) | − | 296.292i | − | 0.382313i | ||||||
\(776\) | −111.406 | − | 736.513i | −0.143564 | − | 0.949114i | ||||
\(777\) | 5.56667 | 0.00716432 | ||||||||
\(778\) | −1047.07 | + | 676.532i | −1.34585 | + | 0.869578i | ||||
\(779\) | − | 282.460i | − | 0.362593i | ||||||
\(780\) | −332.060 | − | 149.692i | −0.425719 | − | 0.191913i | ||||
\(781\) | 549.512 | 0.703600 | ||||||||
\(782\) | 138.491 | + | 214.343i | 0.177098 | + | 0.274096i | ||||
\(783\) | − | 185.365i | − | 0.236736i | ||||||
\(784\) | −515.402 | − | 583.200i | −0.657400 | − | 0.743877i | ||||
\(785\) | −397.098 | −0.505858 | ||||||||
\(786\) | −184.718 | + | 119.349i | −0.235011 | + | 0.151844i | ||||
\(787\) | 825.185i | 1.04852i | 0.851558 | + | 0.524260i | \(0.175658\pi\) | ||||
−0.851558 | + | 0.524260i | \(0.824342\pi\) | |||||||
\(788\) | 123.117 | − | 273.110i | 0.156240 | − | 0.346586i | ||||
\(789\) | −177.946 | −0.225533 | ||||||||
\(790\) | 159.868 | + | 247.429i | 0.202364 | + | 0.313201i | ||||
\(791\) | 38.7971i | 0.0490482i | ||||||||
\(792\) | −220.206 | + | 33.3087i | −0.278038 | + | 0.0420564i | ||||
\(793\) | 205.309 | 0.258902 | ||||||||
\(794\) | −597.106 | + | 385.799i | −0.752022 | + | 0.485893i | ||||
\(795\) | − | 9.88087i | − | 0.0124288i | ||||||
\(796\) | 917.500 | + | 413.606i | 1.15264 | + | 0.519606i | ||||
\(797\) | 1113.70 | 1.39737 | 0.698684 | − | 0.715430i | \(-0.253769\pi\) | ||||
0.698684 | + | 0.715430i | \(0.253769\pi\) | |||||||
\(798\) | 7.90356 | + | 12.2324i | 0.00990421 | + | 0.0153288i | ||||
\(799\) | − | 294.388i | − | 0.368445i | ||||||
\(800\) | −154.058 | − | 43.2000i | −0.192572 | − | 0.0540000i | ||||
\(801\) | 391.398 | 0.488637 | ||||||||
\(802\) | −912.043 | + | 589.285i | −1.13721 | + | 0.734770i | ||||
\(803\) | − | 770.226i | − | 0.959186i | ||||||
\(804\) | −198.563 | + | 440.471i | −0.246969 | + | 0.547849i | ||||
\(805\) | −42.7907 | −0.0531561 | ||||||||
\(806\) | 1512.23 | + | 2340.50i | 1.87622 | + | 2.90384i | ||||
\(807\) | − | 214.161i | − | 0.265379i | ||||||
\(808\) | 4.38009 | + | 28.9571i | 0.00542090 | + | 0.0358380i | ||||
\(809\) | −1049.54 | −1.29733 | −0.648664 | − | 0.761075i | \(-0.724672\pi\) | ||||
−0.648664 | + | 0.761075i | \(0.724672\pi\) | |||||||
\(810\) | 33.8066 | − | 21.8430i | 0.0417365 | − | 0.0269666i | ||||
\(811\) | − | 424.482i | − | 0.523406i | −0.965148 | − | 0.261703i | \(-0.915716\pi\) | ||
0.965148 | − | 0.261703i | \(-0.0842841\pi\) | |||||||
\(812\) | 77.6018 | + | 34.9827i | 0.0955688 | + | 0.0430821i | ||||
\(813\) | 575.683 | 0.708097 | ||||||||
\(814\) | −54.2638 | − | 83.9847i | −0.0666632 | − | 0.103175i | ||||
\(815\) | − | 216.625i | − | 0.265798i | ||||||
\(816\) | 82.5959 | − | 72.9940i | 0.101220 | − | 0.0894534i | ||||
\(817\) | 254.528 | 0.311540 | ||||||||
\(818\) | −182.259 | + | 117.761i | −0.222811 | + | 0.143962i | ||||
\(819\) | 42.0769i | 0.0513760i | ||||||||
\(820\) | 147.323 | − | 326.807i | 0.179663 | − | 0.398545i | ||||
\(821\) | −1257.98 | −1.53225 | −0.766126 | − | 0.642690i | \(-0.777818\pi\) | ||||
−0.766126 | + | 0.642690i | \(0.777818\pi\) | |||||||
\(822\) | −259.728 | − | 401.983i | −0.315970 | − | 0.489031i | ||||
\(823\) | − | 729.181i | − | 0.886004i | −0.896521 | − | 0.443002i | \(-0.853913\pi\) | ||
0.896521 | − | 0.443002i | \(-0.146087\pi\) | |||||||
\(824\) | −1197.71 | + | 181.167i | −1.45353 | + | 0.219863i | ||||
\(825\) | −80.3639 | −0.0974108 | ||||||||
\(826\) | −36.4792 | + | 23.5698i | −0.0441637 | + | 0.0285349i | ||||
\(827\) | 72.5882i | 0.0877729i | 0.999037 | + | 0.0438865i | \(0.0139740\pi\) | ||||
−0.999037 | + | 0.0438865i | \(0.986026\pi\) | |||||||
\(828\) | −350.941 | − | 158.203i | −0.423842 | − | 0.191067i | ||||
\(829\) | 900.257 | 1.08596 | 0.542978 | − | 0.839747i | \(-0.317297\pi\) | ||||
0.542978 | + | 0.839747i | \(0.317297\pi\) | |||||||
\(830\) | 315.289 | + | 487.977i | 0.379867 | + | 0.587924i | ||||
\(831\) | − | 218.093i | − | 0.262447i | ||||||
\(832\) | 1437.43 | − | 445.038i | 1.72768 | − | 0.534901i | ||||
\(833\) | 193.482 | 0.232272 | ||||||||
\(834\) | 87.1653 | − | 56.3189i | 0.104515 | − | 0.0675286i | ||||
\(835\) | 341.235i | 0.408664i | ||||||||
\(836\) | 107.507 | − | 238.483i | 0.128597 | − | 0.285266i | ||||
\(837\) | −307.916 | −0.367881 | ||||||||
\(838\) | −186.877 | − | 289.232i | −0.223004 | − | 0.345145i | ||||
\(839\) | − | 71.4721i | − | 0.0851872i | −0.999092 | − | 0.0425936i | \(-0.986438\pi\) | ||
0.999092 | − | 0.0425936i | \(-0.0135621\pi\) | |||||||
\(840\) | 2.76433 | + | 18.2752i | 0.00329087 | + | 0.0217562i | ||||
\(841\) | 431.594 | 0.513191 | ||||||||
\(842\) | 803.851 | − | 519.381i | 0.954693 | − | 0.616842i | ||||
\(843\) | 91.0414i | 0.107997i | ||||||||
\(844\) | 832.165 | + | 375.138i | 0.985978 | + | 0.444476i | ||||
\(845\) | 858.201 | 1.01562 | ||||||||
\(846\) | 240.998 | + | 372.995i | 0.284868 | + | 0.440893i | ||||
\(847\) | 20.8124i | 0.0245719i | ||||||||
\(848\) | 27.0312 | + | 30.5870i | 0.0318764 | + | 0.0360695i | ||||
\(849\) | 345.178 | 0.406570 | ||||||||
\(850\) | 33.4083 | − | 21.5857i | 0.0393039 | − | 0.0253949i | ||||
\(851\) | − | 172.831i | − | 0.203091i | ||||||
\(852\) | 168.607 | − | 374.020i | 0.197896 | − | 0.438991i | ||||
\(853\) | 882.349 | 1.03441 | 0.517203 | − | 0.855862i | \(-0.326973\pi\) | ||||
0.517203 | + | 0.855862i | \(0.326973\pi\) | |||||||
\(854\) | −5.65391 | − | 8.75061i | −0.00662050 | − | 0.0102466i | ||||
\(855\) | 47.2765i | 0.0552941i | ||||||||
\(856\) | −655.022 | + | 99.0796i | −0.765213 | + | 0.115747i | ||||
\(857\) | −370.111 | −0.431868 | −0.215934 | − | 0.976408i | \(-0.569280\pi\) | ||||
−0.215934 | + | 0.976408i | \(0.569280\pi\) | |||||||
\(858\) | 634.817 | − | 410.165i | 0.739880 | − | 0.478048i | ||||
\(859\) | 1039.00i | 1.20955i | 0.796397 | + | 0.604774i | \(0.206736\pi\) | ||||
−0.796397 | + | 0.604774i | \(0.793264\pi\) | |||||||
\(860\) | 294.489 | + | 132.755i | 0.342429 | + | 0.154366i | ||||
\(861\) | −41.4112 | −0.0480966 | ||||||||
\(862\) | −315.546 | − | 488.373i | −0.366062 | − | 0.566558i | ||||
\(863\) | − | 72.0666i | − | 0.0835071i | −0.999128 | − | 0.0417535i | \(-0.986706\pi\) | ||
0.999128 | − | 0.0417535i | \(-0.0132944\pi\) | |||||||
\(864\) | −44.8948 | + | 160.101i | −0.0519616 | + | 0.185303i | ||||
\(865\) | 348.319 | 0.402681 | ||||||||
\(866\) | 90.3306 | − | 58.3640i | 0.104308 | − | 0.0673950i | ||||
\(867\) | − | 473.161i | − | 0.545745i | ||||||
\(868\) | 58.1110 | − | 128.907i | 0.0669482 | − | 0.148511i | ||||
\(869\) | −611.254 | −0.703399 | ||||||||
\(870\) | 149.960 | + | 232.094i | 0.172368 | + | 0.266775i | ||||
\(871\) | − | 1639.66i | − | 1.88250i | ||||||
\(872\) | 8.81609 | + | 58.2838i | 0.0101102 | + | 0.0668393i | ||||
\(873\) | −279.334 | −0.319970 | ||||||||
\(874\) | 379.785 | − | 245.385i | 0.434536 | − | 0.280761i | ||||
\(875\) | 6.66951i | 0.00762230i | ||||||||
\(876\) | −524.247 | − | 236.329i | −0.598456 | − | 0.269782i | ||||
\(877\) | 14.4444 | 0.0164703 | 0.00823514 | − | 0.999966i | \(-0.497379\pi\) | ||||
0.00823514 | + | 0.999966i | \(0.497379\pi\) | |||||||
\(878\) | 356.720 | + | 552.099i | 0.406287 | + | 0.628815i | ||||
\(879\) | 176.948i | 0.201306i | ||||||||
\(880\) | 248.772 | − | 219.852i | 0.282696 | − | 0.249832i | ||||
\(881\) | 1589.22 | 1.80388 | 0.901942 | − | 0.431858i | \(-0.142142\pi\) | ||||
0.901942 | + | 0.431858i | \(0.142142\pi\) | |||||||
\(882\) | −245.146 | + | 158.393i | −0.277944 | + | 0.179584i | ||||
\(883\) | 495.149i | 0.560758i | 0.959889 | + | 0.280379i | \(0.0904601\pi\) | ||||
−0.959889 | + | 0.280379i | \(0.909540\pi\) | |||||||
\(884\) | −153.732 | + | 341.022i | −0.173905 | + | 0.385772i | ||||
\(885\) | −140.987 | −0.159307 | ||||||||
\(886\) | 465.533 | + | 720.510i | 0.525432 | + | 0.813216i | ||||
\(887\) | 1384.20i | 1.56054i | 0.625440 | + | 0.780272i | \(0.284919\pi\) | ||||
−0.625440 | + | 0.780272i | \(0.715081\pi\) | |||||||
\(888\) | −73.8132 | + | 11.1651i | −0.0831230 | + | 0.0125733i | ||||
\(889\) | 83.1988 | 0.0935870 | ||||||||
\(890\) | −490.068 | + | 316.641i | −0.550638 | + | 0.355776i | ||||
\(891\) | 83.5166i | 0.0937336i | ||||||||
\(892\) | −313.443 | − | 141.299i | −0.351393 | − | 0.158407i | ||||
\(893\) | −521.611 | −0.584111 | ||||||||
\(894\) | −89.0760 | − | 137.864i | −0.0996376 | − | 0.154210i | ||||
\(895\) | − | 281.746i | − | 0.314800i | ||||||
\(896\) | −58.5528 | − | 49.0099i | −0.0653491 | − | 0.0546985i | ||||
\(897\) | 1306.38 | 1.45639 | ||||||||
\(898\) | 687.448 | − | 444.171i | 0.765533 | − | 0.494623i | ||||
\(899\) | − | 2113.95i | − | 2.35145i | ||||||
\(900\) | −24.6581 | + | 54.6990i | −0.0273979 | + | 0.0607766i | ||||
\(901\) | −10.1475 | −0.0112625 | ||||||||
\(902\) | 403.676 | + | 624.773i | 0.447534 | + | 0.692653i | ||||
\(903\) | − | 37.3161i | − | 0.0413246i | ||||||
\(904\) | −77.8155 | − | 514.444i | −0.0860791 | − | 0.569075i | ||||
\(905\) | −775.300 | −0.856685 | ||||||||
\(906\) | −318.903 | + | 206.049i | −0.351991 | + | 0.227427i | ||||
\(907\) | − | 957.750i | − | 1.05595i | −0.849259 | − | 0.527977i | \(-0.822951\pi\) | ||
0.849259 | − | 0.527977i | \(-0.177049\pi\) | |||||||
\(908\) | 1029.64 | + | 464.160i | 1.13397 | + | 0.511189i | ||||
\(909\) | 10.9824 | 0.0120819 | ||||||||
\(910\) | −34.0402 | − | 52.6844i | −0.0374068 | − | 0.0578949i | ||||
\(911\) | 704.979i | 0.773852i | 0.922111 | + | 0.386926i | \(0.126463\pi\) | ||||
−0.922111 | + | 0.386926i | \(0.873537\pi\) | |||||||
\(912\) | −129.335 | − | 146.348i | −0.141814 | − | 0.160469i | ||||
\(913\) | −1205.51 | −1.32038 | ||||||||
\(914\) | 1291.08 | − | 834.185i | 1.41256 | − | 0.912675i | ||||
\(915\) | − | 33.8198i | − | 0.0369615i | ||||||
\(916\) | 227.287 | − | 504.189i | 0.248130 | − | 0.550424i | ||||
\(917\) | −37.8717 | −0.0412996 | ||||||||
\(918\) | −22.4325 | − | 34.7190i | −0.0244362 | − | 0.0378202i | ||||
\(919\) | 607.048i | 0.660553i | 0.943884 | + | 0.330277i | \(0.107142\pi\) | ||||
−0.943884 | + | 0.330277i | \(0.892858\pi\) | |||||||
\(920\) | 567.398 | − | 85.8254i | 0.616737 | − | 0.0932884i | ||||
\(921\) | 568.790 | 0.617578 | ||||||||
\(922\) | −531.782 | + | 343.593i | −0.576770 | + | 0.372660i | ||||
\(923\) | 1392.29i | 1.50844i | ||||||||
\(924\) | −34.9638 | − | 15.7616i | −0.0378396 | − | 0.0170580i | ||||
\(925\) | −26.9380 | −0.0291222 | ||||||||
\(926\) | −533.151 | − | 825.163i | −0.575757 | − | 0.891104i | ||||
\(927\) | 454.250i | 0.490022i | ||||||||
\(928\) | −1099.15 | − | 308.219i | −1.18443 | − | 0.332132i | ||||
\(929\) | 1011.21 | 1.08849 | 0.544247 | − | 0.838925i | \(-0.316815\pi\) | ||||
0.544247 | + | 0.838925i | \(0.316815\pi\) | |||||||
\(930\) | 385.540 | − | 249.104i | 0.414560 | − | 0.267854i | ||||
\(931\) | − | 342.822i | − | 0.368230i | ||||||
\(932\) | −0.859647 | + | 1.90695i | −0.000922368 | + | 0.00204608i | ||||
\(933\) | 165.303 | 0.177174 | ||||||||
\(934\) | −445.434 | − | 689.403i | −0.476910 | − | 0.738119i | ||||
\(935\) | 82.5328i | 0.0882704i | ||||||||
\(936\) | −84.3938 | − | 557.934i | −0.0901643 | − | 0.596083i | ||||
\(937\) | −363.105 | −0.387519 | −0.193760 | − | 0.981049i | \(-0.562068\pi\) | ||||
−0.193760 | + | 0.981049i | \(0.562068\pi\) | |||||||
\(938\) | −69.8846 | + | 45.1536i | −0.0745039 | + | 0.0481381i | ||||
\(939\) | 953.334i | 1.01527i | ||||||||
\(940\) | −603.505 | − | 272.058i | −0.642027 | − | 0.289424i | ||||
\(941\) | −1106.51 | −1.17588 | −0.587942 | − | 0.808903i | \(-0.700061\pi\) | ||||
−0.587942 | + | 0.808903i | \(0.700061\pi\) | |||||||
\(942\) | −333.855 | − | 516.711i | −0.354411 | − | 0.548525i | ||||
\(943\) | 1285.71i | 1.36342i | ||||||||
\(944\) | 436.435 | − | 385.698i | 0.462325 | − | 0.408579i | ||||
\(945\) | 6.93116 | 0.00733456 | ||||||||
\(946\) | −562.990 | + | 363.757i | −0.595127 | + | 0.384521i | ||||
\(947\) | − | 553.561i | − | 0.584541i | −0.956336 | − | 0.292271i | \(-0.905589\pi\) | ||
0.956336 | − | 0.292271i | \(-0.0944108\pi\) | |||||||
\(948\) | −187.552 | + | 416.044i | −0.197839 | + | 0.438865i | ||||
\(949\) | 1951.51 | 2.05639 | ||||||||
\(950\) | −38.2466 | − | 59.1947i | −0.0402596 | − | 0.0623102i | ||||
\(951\) | 761.053i | 0.800266i | ||||||||
\(952\) | 18.7684 | − | 2.83894i | 0.0197147 | − | 0.00298208i | ||||
\(953\) | −1674.84 | −1.75744 | −0.878718 | − | 0.477342i | \(-0.841600\pi\) | ||||
−0.878718 | + | 0.477342i | \(0.841600\pi\) | |||||||
\(954\) | 12.8571 | − | 8.30720i | 0.0134771 | − | 0.00870776i | ||||
\(955\) | 297.753i | 0.311783i | ||||||||
\(956\) | 268.728 | + | 121.142i | 0.281096 | + | 0.126717i | ||||
\(957\) | −573.371 | −0.599134 | ||||||||
\(958\) | −215.902 | − | 334.154i | −0.225368 | − | 0.348804i | ||||
\(959\) | − | 82.4162i | − | 0.0859398i | ||||||
\(960\) | −73.3093 | − | 236.782i | −0.0763638 | − | 0.246648i | ||||
\(961\) | −2550.57 | −2.65408 | ||||||||
\(962\) | 212.791 | − | 137.488i | 0.221196 | − | 0.142919i | ||||
\(963\) | 248.428i | 0.257973i | ||||||||
\(964\) | 51.5692 | − | 114.396i | 0.0534950 | − | 0.118668i | ||||
\(965\) | −304.656 | −0.315706 | ||||||||
\(966\) | −35.9757 | − | 55.6799i | −0.0372419 | − | 0.0576396i | ||||
\(967\) | 786.720i | 0.813568i | 0.913524 | + | 0.406784i | \(0.133350\pi\) | ||||
−0.913524 | + | 0.406784i | \(0.866650\pi\) | |||||||
\(968\) | −41.7435 | − | 275.969i | −0.0431234 | − | 0.285092i | ||||
\(969\) | 48.5524 | 0.0501057 | ||||||||
\(970\) | 349.753 | − | 225.981i | 0.360570 | − | 0.232970i | ||||
\(971\) | − | 1289.75i | − | 1.32827i | −0.747612 | − | 0.664135i | \(-0.768800\pi\) | ||
0.747612 | − | 0.664135i | \(-0.231200\pi\) | |||||||
\(972\) | 56.8448 | + | 25.6255i | 0.0584823 | + | 0.0263637i | ||||
\(973\) | 17.8710 | 0.0183669 | ||||||||
\(974\) | 222.246 | + | 343.972i | 0.228178 | + | 0.353154i | ||||
\(975\) | − | 203.617i | − | 0.208838i | ||||||
\(976\) | 92.5210 | + | 104.692i | 0.0947961 | + | 0.107266i | ||||
\(977\) | 495.847 | 0.507520 | 0.253760 | − | 0.967267i | \(-0.418333\pi\) | ||||
0.253760 | + | 0.967267i | \(0.418333\pi\) | |||||||
\(978\) | 281.876 | − | 182.125i | 0.288217 | − | 0.186222i | ||||
\(979\) | − | 1210.68i | − | 1.23665i | ||||||
\(980\) | 178.807 | − | 396.646i | 0.182456 | − | 0.404741i | ||||
\(981\) | 22.1051 | 0.0225332 | ||||||||
\(982\) | −855.933 | − | 1324.74i | −0.871622 | − | 1.34902i | ||||
\(983\) | 967.035i | 0.983759i | 0.870663 | + | 0.491880i | \(0.163690\pi\) | ||||
−0.870663 | + | 0.491880i | \(0.836310\pi\) | |||||||
\(984\) | 549.106 | − | 83.0585i | 0.558035 | − | 0.0844091i | ||||
\(985\) | 167.469 | 0.170019 | ||||||||
\(986\) | 238.358 | − | 154.007i | 0.241742 | − | 0.156194i | ||||
\(987\) | 76.4730i | 0.0774803i | ||||||||
\(988\) | 604.241 | + | 272.390i | 0.611580 | + | 0.275698i | ||||
\(989\) | −1158.57 | −1.17145 | ||||||||
\(990\) | −67.5649 | − | 104.571i | −0.0682473 | − | 0.105627i | ||||
\(991\) | 1203.68i | 1.21461i | 0.794469 | + | 0.607305i | \(0.207749\pi\) | ||||
−0.794469 | + | 0.607305i | \(0.792251\pi\) | |||||||
\(992\) | −511.994 | + | 1825.84i | −0.516123 | + | 1.84057i | ||||
\(993\) | 831.249 | 0.837109 | ||||||||
\(994\) | 59.3417 | − | 38.3416i | 0.0596999 | − | 0.0385730i | ||||
\(995\) | 562.605i | 0.565432i | ||||||||
\(996\) | −369.888 | + | 820.519i | −0.371373 | + | 0.823814i | ||||
\(997\) | −1274.55 | −1.27838 | −0.639192 | − | 0.769047i | \(-0.720731\pi\) | ||||
−0.639192 | + | 0.769047i | \(0.720731\pi\) | |||||||
\(998\) | −803.603 | − | 1243.74i | −0.805214 | − | 1.24624i | ||||
\(999\) | 27.9948i | 0.0280228i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 60.3.c.a.31.5 | ✓ | 8 | |
3.2 | odd | 2 | 180.3.c.b.91.4 | 8 | |||
4.3 | odd | 2 | inner | 60.3.c.a.31.6 | yes | 8 | |
5.2 | odd | 4 | 300.3.f.b.199.14 | 16 | |||
5.3 | odd | 4 | 300.3.f.b.199.3 | 16 | |||
5.4 | even | 2 | 300.3.c.d.151.4 | 8 | |||
8.3 | odd | 2 | 960.3.e.c.511.6 | 8 | |||
8.5 | even | 2 | 960.3.e.c.511.1 | 8 | |||
12.11 | even | 2 | 180.3.c.b.91.3 | 8 | |||
15.2 | even | 4 | 900.3.f.f.199.3 | 16 | |||
15.8 | even | 4 | 900.3.f.f.199.14 | 16 | |||
15.14 | odd | 2 | 900.3.c.u.451.5 | 8 | |||
20.3 | even | 4 | 300.3.f.b.199.13 | 16 | |||
20.7 | even | 4 | 300.3.f.b.199.4 | 16 | |||
20.19 | odd | 2 | 300.3.c.d.151.3 | 8 | |||
24.5 | odd | 2 | 2880.3.e.j.2431.7 | 8 | |||
24.11 | even | 2 | 2880.3.e.j.2431.6 | 8 | |||
60.23 | odd | 4 | 900.3.f.f.199.4 | 16 | |||
60.47 | odd | 4 | 900.3.f.f.199.13 | 16 | |||
60.59 | even | 2 | 900.3.c.u.451.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.3.c.a.31.5 | ✓ | 8 | 1.1 | even | 1 | trivial | |
60.3.c.a.31.6 | yes | 8 | 4.3 | odd | 2 | inner | |
180.3.c.b.91.3 | 8 | 12.11 | even | 2 | |||
180.3.c.b.91.4 | 8 | 3.2 | odd | 2 | |||
300.3.c.d.151.3 | 8 | 20.19 | odd | 2 | |||
300.3.c.d.151.4 | 8 | 5.4 | even | 2 | |||
300.3.f.b.199.3 | 16 | 5.3 | odd | 4 | |||
300.3.f.b.199.4 | 16 | 20.7 | even | 4 | |||
300.3.f.b.199.13 | 16 | 20.3 | even | 4 | |||
300.3.f.b.199.14 | 16 | 5.2 | odd | 4 | |||
900.3.c.u.451.5 | 8 | 15.14 | odd | 2 | |||
900.3.c.u.451.6 | 8 | 60.59 | even | 2 | |||
900.3.f.f.199.3 | 16 | 15.2 | even | 4 | |||
900.3.f.f.199.4 | 16 | 60.23 | odd | 4 | |||
900.3.f.f.199.13 | 16 | 60.47 | odd | 4 | |||
900.3.f.f.199.14 | 16 | 15.8 | even | 4 | |||
960.3.e.c.511.1 | 8 | 8.5 | even | 2 | |||
960.3.e.c.511.6 | 8 | 8.3 | odd | 2 | |||
2880.3.e.j.2431.6 | 8 | 24.11 | even | 2 | |||
2880.3.e.j.2431.7 | 8 | 24.5 | odd | 2 |